The following is a presentation of TFNN The Traders Edge with Steve Rhodes Toll free at 1-877-927-6648 or internationally at<PHONE_NUMBER> The Traders Edge now Steve Rhodes Good afternoon folks. Welcome to the October 13th. The wonderful Wednesday edition of today's Traders Edge show. I'm your host DB Perseverance Rhodes Who absolutely knows that each of us should always be pioneers of our future versus prisoners of our past Hope everyone out there is having a great day. Hey, let's make sure we have an extraordinary one and the easiest way to do that Always remember that life is happening for us not to us That's right. We need to make that one little two-by-four ship Means we can find the gift in every set of circumstance that life is gonna toss at us now today You and I we're gonna go check out the circumstance of these markets We'll go figure out what those bulls and bears what those buyers and sellers are communicating to you And I just passed one o'clock in the afternoon. I want you to know I'm absolutely grateful for your presence here But more important than that. That's this during this next 60 minutes. I'm here to serve you So feel free to pick up that phone you can give us called eight seven seven nine two seven six six four eight If you can't call in we've got you covered You can always let those fingers do the walking go ahead send me an email send it to Steve at tfnn.com Inside the subject heading if you'd be kind enough to put radio show question in and our Tigers Den any ping will do So let's go ahead and get this show started a wonderful Wednesday. Of course, this is Tiger financial news network I'm Steve Rhodes. Welcome to last show right now a little bit of a mixed bag out You got the Dow Jones index and the Dow Transports the only two indices trading to the downside of 61 and 53 points respectively Not a significant percentage to the downside the S&P not a significant percentage the upside She's up two points the NDX about a half a percent or 70 points Russell's up to that's flat Some eyes are up 17 Goldilocks the big move there. It's up 36 bucks trading at 1795 silver 64 pennies 2315 their gold back 18 pennies straight out at 80 46 lead the charge dollar wise to the upside Ricardo Lee Ray up 44 bucks Shopify 33 black rep 31 Amazon up 26 and C limited is up 25 Bucca runes to the downside is bone biologics off 13 bucks 73 percent yikes Serepta therapeutics is that hold on I'm gonna get all the way to the top a line technologies off 42 then bone is down 13 then you got Serepta off 10 11 percent Avis is down 8 and American Express is down 7 buck runes So that's what's going on there. What is going on in your world? Let's go take a look at hey I think we've got this as with regard to the markets here. I can boil it down to two numbers Just two numbers to be watching to either the upside or to the downside So let's go take a look at that chart Then we go take a look at everything else out here those two numbers and I'm referring to the ES many and I'm looking At a 60-minute time frame now the reason that I say that this is the chart to be paying attention to at least during the day Here is because the chart patterns that are out here So this forms a teeny nine count top it does a bar generates bar number eight at six o'clock this morning Five o'clock my apology bar number nine completes at 6 a.m. That is the key resistance level that resistance level is 43 Sorry, I don't know how that happened. It is 40. What the heck? It is 43 53 75 43 53 75 if the ESP Closes above that then we should anticipate and move up to the 43 85 level the downside support area is 43 23 25 that was established by the TD nine count pattern out here We can see that earlier this morning at about 11 o'clock on the pullback. That is where price found support So the only two numbers that you need to pay attention to today Otherwise, all that we're seeing is just more consolidation type work out here in between those two price point levels out there So that's what we'll continue to focus on during the day. We've got a caller on the line. It's brent de martinez california brent Thanks for calling. Thanks for holding. How are you doing this morning? I'm doing quite well, Stephen you Excellent. Thanks much for asking and GFI. I believe is what you're calling about. That's the gold fields I believe uh, tell me what you're doing and how I can best help you We've talked about this not too long ago. I'm in there around 8 50 and uh I just seem like there was a level I think it might have I mean depends on our clothes today, of course a little earlier that No for sure, but I have at this point in either uh bar 10 or this could be bar one to pin on the clothes today So it's kind of basically recycling the count again on the daily and then on the weekly I think it's only in bar two, but if we could take a look at that and just what are there areas Above that I need to watch Absolutely, okay, so we're going to go take the gold fields and we're going to pull the white background charts out here And brent is absolutely correct. Today is going to be the bar following bar number nine So that's a cool, um element to this chart out here. That is a topping signal Uh does not mean that this chart will top. In fact, what I like to do brent is take a look at You know, whenever td nine count patterns form I like to go back and just kind of take a look at a brief history of the chart This one just takes me back into december of 2020 and to see if there's any other td nine counts that formed And just simply how well Did the uh did the market behave when those patterns formed and in the case of gold fields I don't see where necessarily respects the td nine count pattern as well So all that that means doesn't mean that it can't top because it most certainly can Uh what it does mean to me is whatever today's high is is going to be a key level to watch If price closes above that high tomorrow and right now the high inside of gold fields is up at the 945 level if price is able to close above that then the signal is a move back to 10 52 So you're absolutely right It's got a td nine count top that's going to be in place today It's just that when I go back and I take a look at other td nine count patterns out here Now look at the very high out here on the trading day of june 1st not the very high No, that was not even a td nine count top. So yeah, so i'm not going to get too hung up on gold fields With regard to the td nine count tops that makes sense on the daily chart Yes, it does Steve Okay, perfect. So let's go take a look at the weekly time frame. So on the weekly time frame, yeah I believe you said bar number two. You're absolutely correct now The cool thing about this chart or this pattern Or what we're looking at out here and unfortunately, it's only wednesday at 113 in the afternoon But price right now is trading above the top of a brand new bear instruction weekly profile that began forming last week And that top is at 9 20. So if price can close above 9 20 on friday Brent that would be another bullish indication I put that together with price closing above whatever the high is today Both of those two things would be a positive outcome for gold fields with regard to where's the next resistance level I'd have to come to take a look at the monthly time frame chart and look at $10 18 cents That is the oscillator and change line for that time frame a quick peek at short term charts out here We'll see a roadsman to mitigate our top and gold fields for the 30 minute time frame But price has held its oscillator and change line. That's currently printed at 9 35 If you were to see a close below 9 35, you know during the rest of the afternoon You'd expect a retracement that retracement could take you all the way back to 9 14 But right now that is not the message Brent. Is there any additional information that uh, I can provide you with uh regard to gold fields No, that's great. And I guess, you know, there's I had like I did last time If you can look at gdx, I could even just listen to that offline, but um, we'll just do right now if you Yeah, okay Yeah, just if you've got the question others have the question too. So in the case of the gdx Uh, it is going to form bar number eight today Uh, we are going to the break if you want I could just review this and you can listen in or Feel free to stay on and ask any questions. Totally up to you. Just let the guys in the production room. No I'm gonna stay on the line Perfect. Sounds great. We'll be back with Brent in about three to four minutes. Hope states Steve Rhodes started his trading career as a student almost 20 years ago And the student has now become the master Steve won the prestigious timer of the year award in 2018 And barely missed that mark again in 2019 finishing at number two for the year an amazing accomplishment Steve Rhodes is committed to sharing his techniques and knowledge with anyone who wants to learn And he shares his vast amount of trading knowledge every day in his mastering probability newsletter Steve's award-winning newsletter Mastering probability is delivered every trading day with updates throughout the afternoon sign up for steve's market newsletter Mastering probability and you'll receive access to seven of steve's educational webinars Absolutely free at tfnn all our newsletters come with a 30 day money back guarantee So you have absolutely nothing to worry about visit tfnn.com and try mastering probability 30 days risk-free today tfnn educating investors What's separating you from the most successful men and women on wall street? 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So likely that'll take it out now the a to b equal cd Price projection tool gives us a one to one Target of 3304, but this retracement was only 33 percent So odds favor that this is going to be an extension a 11.272, which can take it to 33 73 the 618 That's the 1.6 when it takes us to 34 60 So those become price target levels in the meantime though We're going to go take a look at our white background charts and see if there's any kind of detour signs And this is where today is going to form bar number 8 of a td9 count And we do know that on these td9 counts that price can go ahead and form its top or bottom In this case here, we're looking at tops on bars 8 9 to the bar following 9 Now brent, even though the gdx shows that today is going to become bar number 8 I don't believe that this is the high of the pattern And the reason is is that if we was if I was going to pull over The x au chart in order for me to do that I've got to change tabs and everything so you just have to trust me on this Or during the 2 o'clock update is when I show the indices It's only in bar number 7 And I think that the x au is the better reference point than the gdx are both good out here But i'm not sensing that today will be the high of the pattern Especially with the a to b equals cd but anything can happen But price is taking out a resistance level. That's 31 56. That's the td9 breakdown level on the daily basis So that looks very positive any questions about the daily chart So far or the a to b equals cd pattern that we took a look at I think that might have been the one there was one other level. I know that we it would be nice to get above and it was I think at the time I could have changed was like, you know, 31 78 something like that And I could have been on the weekly could have been the one you just mentioned. I'm not positive But that's that's what I was going to ask you about Yeah, so there is a new a weekly profile that duff formed or is forming and the resistance level there Brent So it's going to be a new level for us to take a look at is 33 0 5 So if price can close above 33 0 5 that would become a A nice a nice positive But you've got a 33 0 4 You have the 1 1 a to b equals cd in the prior swing point that prior swing point I'm referring to is back on september the 3rd and you got 33 0 5 as a resistance level For the weekly time frame. So that likely becomes the realistic price target for tomorrow and friday. I would say All right. Yeah, no, that's very helpful to you. It's making some progress gold's having a good day We'll just keep an eye on that. So I appreciate it so much to have a great day and have a great rest of the week Thank you. You too. And thanks much for calling that was brent in martinis california We do have a question that's coming by email. So let me get to that that is for federal express fdx is the fdx is the ticker symbol out here and let me get to the question the question is from Michael in virginia. Michael says, can you please look at federal express? We are going to and review for a possible bottom Absolutely. So if we take a look at the black background charts, we can see federal express trading below all profile levels all by when I say all I mean daily weekly and monthly The bottom of daily profile support So price is trading below support now If you look over on the very left hand panel chart, you'll see the daily time frame You will see that a new profile form below price. It's bullish in structure Countertrend moves will typically find the resistance at the center of a bullish structured profile Well, voila if we take a look at the trading session of october 7th, michael That is exactly what took place now price didn't get right up to the center The center was 228 and price got up to a high that day of 227 66 Pretty good for pretty good as far as i'm concerned out there Okay, so that's not going to tell us whether we found a bottom or not But I do want you to know that is an important level 228 26 the price is able to clear that at any point in time You're looking at 233 now. We pull over the white background charts to really help answer michael's question Do we see any kind of bottom signal and the answer is well, that's the week So i'm going to just go with the weekly chart first and excuse me I'm going to try not to sneeze here But you know how you get that little thing it kind of goes up your nose and you're like should I sneeze? Should I not sneeze? I think if I talk about it, maybe I won't sneeze and I don't want to sneeze because yeah I don't have a sneeze button on my mic. Okay. That's that seemed to work Now you guys should try that at home in any event out here on a weekly time frame chart michael You did get a td9 count bottom signal two weeks ago break grapefruit grapefruit. We'll do that You got to explain that a little further out there dan In any event or you just say grapefruit. Is that the deal in any event out here? You do have a td9 count bottom on the weekly time frame You do have an oscillator and change line that three weeks ago went from green to red and that tells us That over time we should anticipate price and that to catch up to each other So the weekly chart is saying yeah, I want to make that move up to that red oscillator and change line It's i'm not saying it's going to get to 254 It could be a combination of things but that line and price should test each other based upon that pattern as well Now when we put up the uh daily time frame out here, what do we got? I'm sure stevo can come up with an a to b equal cd to the downside just as you can So in that case we're going to say yes, michael fedx has put in a bottom It did it with that bolshengolfing candle key reversal session back on the trading day of october the fifth out there The issue the problem is that you know that you've got counter trend resistance at that 228 26 level so what are you going to do? I don't know. Let's uh continue looking at chart See if we can figure this out So i'm just going to look at the short term time frame charts and why take a look at the short term time frame chart For fedx. Well, this is a slight positive That is that right now today michael price is trying to take out a breakdown resistance level from its 30 minute time frame And as at 224 39, how about a 65 minute chart? What do we have out here? You've got the bottom signal back on october 5th. So that looks pretty good. Its resistance is 220 805 The 130 minute time frame chart that also has a bottom resistance here being 226 0 9 or 229 25 and then the 195 minute chart also bottom So the answer is yes fedex is absolutely Attempting to form a bottom What you and I don't know is whether or not price is going to be able to get above that 228 26 level But your question was is there a possible bottom and the charts have answered that question for us So i hope that that helps you out michael. Thanks so much for writing in and folks I'd love to hear from you as well. You can give us a call at<PHONE_NUMBER> or You can send me an email steve at tfnn.com Of course in our tigers den any pig will do so dan says thinking of grapefruit keeps you from sneezing I'm going to be able to put that to the test So that's very cool. Haven't heard of that. Uh, and that's the cool thing I guess here at tfnn is we always learn something new. I love grapefruit To haven't had much. Of course, we're starting. Well, we're a few months away. I think grapefruit season down here In florida starts around the end of january, isn't it? So I tell you one of the coolest If you like oranges, you know, I mean in florida when I moved down here in the early 80s, you know, it was orange uh, orange orchards all over the place uh on highway 60 Which really runs in essence from tampa all the way over to I'd say it's uh like around it's below cocoa. I don't know if it's around it's below melbourne so but Maybe it is cocoa. Anyway, so it's run east and west but in the middle of that is where I think it's minute made. Is that still the name? Anyways, they've got a orange juice processing plant And so if you ever drive down 60 out that way, I mean you just get when they're out there pressing the oranges It's a it's a great smell.  In any event, I'll tell you what's up with that guy. You've got the dow down 23 points s and p's of seven NASDAQ got 83 We'll be right back. We'll go take a look at goldilocks. We get back to this Are you having fun trading the markets? 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We've got the charge for paysafe limited psfe On our screen right now and that is a courtesy of flech inside the tiger's den He's looking at a possible bottom and a trend reversal So we can't see right now. It's trading with inside a bullish structure profile And if it closes today above 723 flech, you should see at least 742 a close above 742 Could give us our change in trend signal But let's go see if we made a bottom if there's any kind of bottoming patterns out here So for that what we do is we go take a look at those white background charts And boom, voila flech is on to something What flech must have spotted was a roadsman to indicator bottom that completed yesterday TD 9 count pattern that completed two days ago And now you're inside a bullish structured profile now price can clear 742 flech the next resistance level will be 798 So the trade looks good so far if price closes above 798 that would be the second change in trend Signal that you would get out there. So that's what we see when we take a look at the daily time frame How about the weekly which is also sold off quite a bit? And let's take a look at the weekly in fact It's basically everybody in this Position is at a loss with the exception of flech out here And so let's go take a look at what the weekly chart is telling us Not much So there's no bottom signal here not much for us to do with regard to that Monthly charts not going to have enough data for us to really sneeze at so to speak Let's take a look at a 30 minute chart out here on the 30 minute basis. What do we have? You got to love it prices broken through giving that initial change in trend signal with a close above 725 So really flech it's all going to be about the daily chart out there You've got the parameters 742 next to close above that expect a little battle at 798 That'll be perhaps a big skirmish and anything above that will give you your change in trend signal So that folks was courtesy of flech inside the tigers den again ticker symbol there a ps fe Let's go to uh, we've got a lot. We got mike and orman beach. Hey mike. Thanks for calling. Thanks for holding. How are you today? Steve i'm doing great. Steve i'm looking at at and t And it looks to me like it may have made a bottom on a daily chart And uh, I looked at it on a 30 minute and it looks like there's a bullish engulfing like right around 10 30 ish This morning. What are your thoughts? Uh on the on the longer term charts? It looks like it may go a little bit lower, but I wanted your opinion Sure, sure. So when we take a look at at and t here's the first thing that we know that stands out Mike and that is that prices trading below the daily weekly and monthly profile So we definitely want to see some kind of bottoming signal out here And as I pull open my white background daily time frame charts I don't the only bottom signal that I would have not I don't know if this is what you're referring to Is wave number seven that's letter g And that will not be confirmed until we see a higher low That forms that could be tomorrow. So that would be a pattern out here that we could Could could significant could indicate a uh a bottom. Let's take a look at the weekly time frame chart. Let's populate this No bottom signal there either. Let's look at the monthly chart. Maybe this gives us a little bit broader picture So on the monthly chart as well, I don't have a bottom signal here for at and t What's going on with them? Hmm in any event? I don't know if you can answer that mike. I can't answer but uh, We took out, um, the lows of last uh, February and march Oh, yeah, no, absolutely. In fact, what's going for is april of 2009 That's what i'm saying. What what what gives what gives her march of 2009 That's where the march of 2009, which was a and that wasn't even a td9 account bottom That appears to be where price is headed to that's in the 21 44 level But back to your 30 minute question out here the 30 minute chart did give you at least an in You know a a tradeable bottom from a day trader standpoint because it did generate a roadsman dominicator Pattern it did that mike at about 11 o'clock this morning now Where's price headed to from here? Same setup as we've been talking about for some of the other instruments. I'll pull this over the side What we can see is there's a bowler structured profile that formed above price So if this is just a counter trend move and there's nothing that I see on the daily weekly or monthly charts to suggest otherwise We should see at and t bounce up to about 25 34 to 25 40 It's really the 25 40 that would be the level that I would be watching Um, because if price turns down from there, that's it's really communicating to a no bottom at all that that That I can see or you know, the charts can see out here So there's no bottom signal that I see other that wave number seven On the daily time frame the 30 minute chart. I'm just looking at the other time frame like 65 or 130 Just seeing if I can find some type of bottom there The 195 minute chart does have a TD 9 count. So it just what it does Signal to me is that more likely than not we should see that move to 25 40 or so That doesn't if price closed above that 25 51 would be next up on the list But with regard to the daily and the weekly, I don't see the bottoming signal other than the other than that wave seven pattern Was there was there what what is the pet can I ask? What's the pattern that you're looking at to think that maybe there's a bottom Maybe I need to go back and take a look at that with you Well, I I've kind of been watching it Because I've been you know trying to you know get it maybe for a longer term hold, you know get a portion of it Okay, and I mean today it looks at this time today on the daily chart. We seem to have it, you know a doji in in in an oversold area And like I said, I you know, I use multiple time frames And then on the 30 which I use It formed that bullish engulfing.  So Sure. So let's let's continue with that thought process. So so with regard to that And right now you're thinking, okay, maybe more of a counter trend than anything else if price were to close About 25 40 we'll just use the 30 minute here because that's really the pattern that that sticks out to both you and I If price close about 25 40 expect 25 51 and price close about 25 51 2603 But does that mean that it's bottomed? I it'd have to see closes You have to see more than just that but with regard to the counter trend rally relief rally or so forth Those would be the numbers that I would be looking for for AT&T. Okay, Mike All right. Thanks and Steve. Thanks for your candlestick education to to teach me a lot of it. So No problem. I use it all the time You've taught us some great things over the years. So thanks Hey, my pleasure. So Mike, I know you're in Ormond Beach and uh, I think was last sunday I happened to stop in steward. So how far and and I caught a caught a jazz show at the Lyric theater Have you ever been to the Lyric theater? Uh, no, I have not Man, what a great what a great, uh, what a great theater So if ever see any kind of show or anything that you want to see Uh, that for you that would be down in steward, right? Yeah. Oh, we're up in Ormond Beach You're up towards Daytona. Uh, what was? Yeah, right, right. What was I thinking? Sorry about that. Well, one thing we do have here at Daytona. They have a band shell Yes, it's an outdoor arena a band shell a lot of times they have Really good bands lately. They've been having tribute bands for a lot of you know famous rockers Everything so that is someplace that uh, I go once in a while And what is what is biker week? What is biker week up there? Uh, we have bike tober fest right now Do like an abbreviated It's actually this week Um, and that goes that goes for about one week, but the main bike week is in uh, march Um, that's the main one that goes for about two weeks Well, I like the sound of bike tober fest. That sounds like a blast. That sounds like a blast Hey, Mike, we're about to go to heartbreak always good to speak to you You have a uh, wonderful wednesday and we'll look forward to talking to you again soon Thanks, Steve. Bye. You bet that was mike in orman beach What was stevie thinking that he was near steward florida not even close steve roads with tfnn You got the dow flat right now s and p is up 14. 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has run its course trade lab u or lab d directions daily s and p biotech three times bull and bear etfs visit direction investments dot com slash biotech today an investor should consider the investment objectives risks charges and expenses of the direction shares carefully before investing the prospectus and summary prospectus contain this and other information about direction shares to obtain a prospectus or summary prospectus please contact direction shares at<PHONE_NUMBER> the prospectus or summary prospectus should be read carefully before investing an investment in the funds is subject to risk including the possible loss of principal the funds are designed to be utilized only by sophisticated investors such as traders and active investors distributor four side fund services llc don't forget you can listen to tfnn live on your mobile device 24 hours per day go to tfnn.com then hit watch tiger tv questions in the queue so let's get to those out here the first one coming from david and tom ball texas he wants to take a look at ticker symbol m o s that is mosaic and uh can he give me a buy point and six month outlook for mosaic so this thing's up at highs i probably can't really give you much of a buy point but we'll see what we can find for you in prices above the top of the daily weekly and monthly profile top of the monthly profile 3823 that's what it's trying to take out as we speak this month we're only what 13 days into the month so no idea what's going to look like on october 31st but we take a look at the daily time frame what we do have out here is a td9 count top that will in fact form today so david this would be a momentum play to the extent that that's how you want to play it this would suggest that price will pull back to test that oscillator and change line now it's printing at 3988 it can't use 3988 is the exact number as price moves up or down that's going to change this a bit so that is your range out there what i would do if you're going to take a look at a momentum trade out there with price pulling back there i would really go down to my short-term time frames like 15 30 65 those would be the ones that i'd be looking at as we look at the 30 minute time frame right now we can see roge mc minicator top price is hovering around the bottom of its 30 minute profile if it closes below this level this level would be 41 13 or 4104 it suggests that price might get back to the 40 18 area 40 18 is a breakout level you would expect that area to hold so that could be another level for you to be watching and observing on the 15 minute chart you've got a td9 count pattern that should form by 145 so by 2 o'clock on just a 15 minute basis you ought to see some kind of bounce where's that bounce take it to probably 41 and a quarter we already talked about the 35 minutes 65 minute chart as roge mc minicator bottom where is its level of support 39 28 is its number out there so it does look like you're going to get some type of retracement inside of mosaic and those would be the areas to be looking at so what i'd be suggesting again to you is look at those short-term time frame charts see if you can find a bottom pattern maybe it's a bottom pattern that you trade out there but that's how i would look at mosaic and i hope that that helps out david thanks so much for writing in the next question coming in from hector and the fuel injectors and hector wants to take a look at the energy sector eat the sec energy sector vs and p500 that is the xle so let's get that punched up on the screen out here let me get that going on my background there we go okay and the question is actually point back on extremely light volume is this a gift from the long-term trading gods to load up the wagon for run into the 74 area out here so a good question let me uh let me see what we've got going on here profile wise above the daily above the weekly and running into resistance at the top of the monthly profile that resistance levels 56 65 let's pull over the other white background charts for energy the energy sector the xle see what we see so we don't have a topping pattern in play at the moment so price is pulling back 5516 is likely its target that's the bottom of its that's the bottom that's its oscillator and changeline uh would i but with this up at its highs like this would i load up the truck probably not the load up the truck should be more towards the bottom and you know than on a momentum play so very much like david in tom ball texas if you're looking for a momentum play though hector uh look for price again pull back towards that 5516 area and then go to a 30 minute timeframe and look for some kind of bottoming pattern out here so on its 30 minute timeframe we can see a td9 count top took place at 11 o'clock that was on october the 11th that's led to an a to b equal cd to the downside that pattern has already been confirmed with this bullish engulfing candle just so that you can visually see the a to b equal cd i'll draw the a to b point then i'm just going to go ahead and take that and i'm going to attach it to the c point and then you can see where the one-to-one came in so here was the projection hit that projection if you get your bullish engulfing candle to 11 o'clock this morning that says hey i should bounce up to the oscillator and changeline and that's all it's been able to do out there so it's not really strong here the xle hector and if price is unable to close up 5634 odds favor move back to about the 5550 level but is it a backup your truck area you know i'd have to say let's go take a look at lights we crude so let's do that because you know that these two are glued to the hip we know that in the case of lights we crude that it's completed a one-to-one move we can we know that just by taking a look at our market update chart so that's in the lower left i'll just expand it out and we won't have to worry to just simply completes the screen so you've got a one-to-one a to b equal cd and if we get a bearish reversal candle and that is inside lights we crude you know that what that says to us that says well to expect and anticipate at least some type of short-term top so when i load up the truck i i i i i i i i struggled to tell somebody to load up the truck when it's really just a momentum play that we're talking taking a look at as we speak right now now on its daily time frame this is the this is the november contract for lights we crude yesterday it triggered a roadsman to mitigate her signal it's a small body candle it was a doji candle so very easy to generate that bearish reversal candle today although a small body candle but if you do get a confirmation of a bearish reversal candle like but mike and i were talking mike and orman beach out there uh that's going to signal a short-term top now that would say price to go target its oscillator and change line 79 20 if price closes below that then you're looking at a move back to 76 46 75 13 7380 and 71 61 those would be the battleground areas on a retracement to the downside out there 75 13 may be the level that you would be looking at it really adding that position of course what you would do here is you do the same kind of thing you go to the short-term time frame charts look for a pattern and then boom you would go ahead and hit it on a weekly basis things look good bar number seven uh but this could also form a roadsman to mitigate her top out there so i'm going to say hector no loading up the truck not just yet well because it would really be a momentum move to do that and uh and so i don't suggest the backing up of the truck so hope that helps out hector thanks so much for writing in both hector and patty they are the fuel injectors michael p writes in and michael wants to take a look at cat so uh let me get out of this chart let's go back to those three panel charts out here let's take a look at caterpillar and uh let's actually type in the proper symbol which is cat that should be easy enough apparently not easy for steve but if we take a look at caterpillar here's what we know price is trading below the daily the weekly and uh tinkering with the bottom of that monthly profile mic that's at 191 81 you're trading 189 63 so not ideal your question is hey steve i'm in cat i sold a call against it and bought it back for profit very nice should i peat or does this look like a bottom good question let's go take a look at caterpillar let's pull over that white background chart uh you know what i'm going to we're going to wait just a moment here i'm going to populate a different set of charts out there there we go and uh pull that back just i've got more timeframes to look at with regard to this set of charts so on the daily time frame your question was do we see a bottom and i don't and i don't think that it's completed the a to b equal cd but let's just make sure let's just draw that a to b point or get pretty close to it and then let's just go take that from the a to b to the c to d and yeah so it hasn't really completed that pattern so um so i'm not going to worry about the gap up the rising window uh so that i don't see on the weekly chart out here uh mic let's go take a look at uh this uh yeah on the weekly i don't see it price right now trading below its breakout level wide 94 39 so this is all suggesting to the extent you're going to hold on to it yeah like what you're doing and on a monthly you've got a roadmap to indicator top and the price is closed below the bottom of that profile this says that caterpillar wants to trade lower so mic i hope that that helps you out as you say i guess it depends on the infrastructure deal yeah maybe uh but right now i think the approach you've taken is the sound approach we don't see a bottom on the daily weekly with monthly time frame charts steep roads with tfnn we'll be back in just a few to close it out sharpening your skills as an investor is like getting better at playing a musical instrument you 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As a final step of statistics and exploring data, I'm going to talk about something that's not usually considered exploring, but is basic descriptive statistics. I like to think of it this way.  And with descriptive statistics, you can think of it as trying to use a little data to stand in for a lot of data, using a few numbers to stand in for a large collection of numbers. And this is consistent with the advice that we get from good old Henry David Thoreau, who told us simplify, simplify. If you can tell your story with more carefully chosen and more informative data, go for it. So there's a few different procedures for doing this. Number one, you want to describe the center of your distribution of data. That's if you're going to pick a single number, use that. Two, if you can give a second number, give something about the spread or the dispersion of the variability. And three, it's also nice to be able to describe the shape of the distribution. Let me say more about each of these in turn. First, let's talk about center, we have the center of our rings here. Now there are a few very common measures of center or location, or central tendency of a distribution. There's the mode, and there's the median, and there's the mean. Now there are many, many others, but those are the ones are going to get you most of the way. Let's talk about the mode first. Now I'm going to create a little data set here on a scale from one to 11. And I'm going to put individual scores. There's a one and another one and another one and another one. Then we have a two, two, then we have a score way over at nine and another score over at 11. So we have eight scores. And this is the distribution. This is actually a histogram of the data set. The mode is the most commonly occurring score or the most frequent score. Well, if you look at how tall each of these go, we've got more ones than anything else. And so one is the mode, because it occurs four times and nothing else comes close to that. The median is a little different. The median is looking for the score that is at the center if you split it into two equal groups. We have eight scores. So we want to get one group of four. That's down here. And then the other group of four is this really big one, because it ranges way out. And the median is going to be the place on the number line that splits those into two groups. That's going to be right here at one and a half. Now, the means a little more complicated, even though people understand means in general, is the first one we have here that actually has a formula where m for the mean is equal to the sum of x. That's our scores on the variable divided by n, the number of scores. You can also write it out with Greek notation if you want like this, where that's sigma, a capital sigma is the summation sign sum of x divided by n. And with our little data set that works out to this one plus one plus one plus one plus two plus two plus nine plus 11. Add those all up and divide by eight, because that's how many scores there are. Well, that reduces to 28 divided by eight, which is equal to 3.5. If you go back to our little chart here, 3.5 is right over here. You'll notice there aren't any scores really exactly right there. That's because the mean tends to get very distorted by outliers. It follows the extreme scores. But a really nice, I say it's more than just a visual analogy, is that if this number line were a seesaw, then the mean is exactly where the balance point or the fulcrum would be for these to be equal. People understand that if somebody weighs more, they got to sit in closer to balance somebody who weighs less who has to sit further out. And that's how the mean works. Now let me give a little bit of the pros and cons of each of these for the mode modes really easy to do you just count how common it is. On the other hand, it may not be close to what appears to be the center of the data. The median, it splits the data into two same size groups the same number of scores in each. And that's pretty easy to deal with. But unfortunately, it's hard to use that information in many statistics after that. And then finally, the mean of these three is the least intuitive. It's the most effective by outliers and skewness. And that may really struck against it, but it is however the most useful statistically. And so it's the one that gets used the most often. Next, there's the issue of spread, spread your tail feathers. And we have a few measures here that are very common also. There's the range. There are percentiles and interquartile range. And there's the variance and the standard deviation. I'll talk about each of those. First, the range, the range is simply the maximum score minus the minimum score. And in our case, that's just 11 minus one, which is equal to 10. So we have a range of 10. And I can show you that here on our chart. It's just that line there at the bottom from the 11 down to the one. That's a range of 10. The interquartile range, which actually is usually referred to simply as the IQR is the distance between Q3, which is the third quartile score and Q1, which is the first quartile score. If you're not familiar with quartiles, it's the same as the 75th percentile score and the 25th percentile score. Really, what it is, is you're going to throw away some of the data. So let's go to our distribution here. First thing we're going to do is we're going to throw away the two highest scores, there they are, they're grayed out now. And then we're going to throw away two of the lowest scores. They're out there. And then we're going to get the range for the remaining ones. Now, this is complicated by the fact that I've got this big gap in between two and nine. And different methods of calculating quartiles do something with that gap. So if you use a spreadsheet, it's actually going to do an interpolation process, and it will give you a value of 3.75, I believe, and then down to one for the first quartile. So not so intuitive with this graph, but that is how it works usually. If you want to write it out, you can do it like this. The interquartile range is equal to q3 minus q1. And in our particular case, that's 3.75 minus one. And that, of course, is equal to just 2.75. And there you have it. Now our final measure of spread or variability or dispersion is two related measures, the variance and the standard deviation.  But the variance, which is at least the easiest formula is this, the variance is equal to that's the sum, the capital sigma is the sum of x minus m, that's how far each individual score is from the mean.  So the variance is the average square deviation from the mean. I'll try to show you that graphically. So here's our data set. And there's our mean right there at three and a half. Let's go to one of these twos, we got a deviation there of one and a half. And if we make a square, that's one and a half points on each side. Well, there it is, we can do a similar square for the other score to if we're going down to one, then it's going to be two and a half squared and that can be that much bigger. And we can draw one of these squares for each of our eight points. The squares for the scores at 911 are going to be huge and go off the page. I'm not going to show them. But once you have all those squares, you add up the area and you get the variance. So this is the formula for the variance. But now let me show the standard deviation, which is also a very common measure is closely related to this. Specifically, it's just the square root of the variance. Now, there's a catch here. The formulas for the variance and the standard deviation are slightly different for populations and samples and that you they use different denominators. But they give similar answers, not identical, but similar if the sample is reasonably large say over 30 or 50, then it's going to be really just a negligible difference. So let's do a little pro and con of these three things. First, the range is very easy to do. It only uses two numbers, the high and the low, but it's determined entirely by those two numbers. And if they're outliers, you've got really a bad situation. The interquartile range or IQ are really good for skewed data. And that's because it ignores extremes on either end. So that's nice. And the variance in the standard deviation, while they are the least intuitive, and they are the most affected by outliers, they are also generally the most useful because they feed into so many other procedures that are used in data science. Finally, let's talk a little bit about the shape of a distribution. You can have symmetrical or skewed distributions, unimodal uniform or u shaped, you can have outliers. There's a lot of variations. Let me show you a few of them. First off is a symmetrical distribution. Pretty easy. They're the same on the left and on the right. And this little pyramid shape is an example of a symmetrical distribution. They're also skewed distributions where most of the scores are on one end and then they taper off. This right here is a positively skewed distribution where most of the scores are at the low end and the outliers are on the high end. This is unimodal. It's our shame pyramid shape. Unimodal means it has one mode or really kind of one hump in the data. That's contrasted, for instance, to bimodal where you have two modes. And that usually happens when you have two distributions got mixed together. There's also uniform distributions where every response is equally common. There's u shaped distributions where people tend to pile up at one end or the other in a big dip in the middle. And so there's a lot of different variations. And you want to get those the shape of the distribution to help you understand and put the numerical summaries like the mean and like that. And you want to get the standard deviation and put those into context. In some we can say this when you use descriptive statistics that allows you to be concise with your data. Tell the story and tell it succinctly. You want to focus on things like the center of the data, the spread of the data, the shape of the data. And above all, watch out for anomalies because they can exercise really undue influence on your interpretation. But this will help you better understand your data and prepare you for the steps that follow.


Live from the Mandalay Bay Convention Center in Las Vegas. It's theCUBE, covering VMworld 2016. Brought to you by VMware and its ecosystem sponsors. Now, here are your hosts, Stu Miniman and John Wall. Well, good morning and welcome to day three here on theCUBE of our coverage of VMworld. We're in the Mandalay Bay and the Convention Center. Been a great three days we've had, looking forward to what we have in store for you on this Wednesday. I'm joined by Stu Miniman here and also with us here on the set is Michelle Borovac who's the Vice President of Marketing for Velostrada. Michelle, good morning to you. And Sasha Sankara, who's the CEO of Rackware. And Sasha, thank you for joining us. Thanks for having me on. You've been with us before on theCUBE. Yeah, you guys did an early interview of women in Silicon Valley. It was a great interview and we really enjoyed it. You guys came to visit our offices too. Well, just to familiarize our audience a little bit about with your individual operations.  Just tell folks a little bit about Velostrada and what you do and in terms of cloud migration and the services that you're providing. Sure, absolutely. So we are a software company that is really focused on helping organizations move workloads from on-premises into the cloud and back. So what's really unique is that we can do that in a matter of minutes instead of weeks or months. Great, and Sasha? Yes, I am the CEO and founder of Rackware. So we do migrations. We also do disaster recovery as a service, backup as a service and things like auto-scaling into the cloud. We're partners with VMware. We're partners with IBM as well. Okay, so one of the big words we've been hearing mentioned a lot at the show is inter-clouding. We've been talking about multi-clouds, hybrid clouds, whether it is actually moving workloads or just managing multiple environments. We actually wrote a couple of years ago. Hybrid cloud is where people are thinking but a lot of it is, I've got composite cloud because I've got applications, lots of different places and managing that is tough. I know you both have commentary on that. Talk to first, what do you think of what VMware talked about this week and kind of the state of where we are, Michelle? Sure, we were very happy to hear on Pat Gelsinger's comments. It is what we've been saying for two years. We certainly believe that companies are really trying to get a handle on public cloud and figure out how do they truly make that an extension of their data center and take advantage of the cost efficiencies of pay as you go. The model makes a lot of sense for certain applications. Sos? Yeah, I fully agree. We've been talking hybrid for years and people sort of laughed at us when we brought it up but when you think about enterprises, there's certain applications that are going to remain on-premise. There's certain ones that are going to go in private cloud and then there's certain applications you're going to put in public cloud. You're going to need sort of a hybrid ecosystem to be able to manage all of that and when you're talking anything, 50, 100 machines, you're not going to put it all in one basket. You're going to spread that out and that equals hybrid. Can you maybe help us unpack when we talk about moving applications or other applications that span certain resources? What's real today? What are some of your more aggressive customers doing? So we have lots of aggressive customers. We sell to the enterprise. We've moved workloads for Procter and Gamble. We've moved workloads for Coca-Cola. We're actually working with HBO on Game of Thrones. This is her that does Game of Thrones so we've migrated lots and lots of workloads but I think there's a little bit of a myth out there. I think if you talk to Amazon, they'll say everybody's going to rewrite their applications. They're not. In the future, they will but there's a lot of existing applications that you need technology like ours to be able to take advantage of the cloud because people don't want to build data centers anymore. People don't want to be in the hardware business anymore. They need to move that out so they can focus on applications and their businesses. And just clarify, you're not only moving to the giant clouds like AWS or Azure but lots of service providers. What's that landscape look like? Yeah, so we've moved Softlayer as a big one, Rackspace. CenturyLink, we've had a long-standing relationship with a variety of clouds and there's the smaller players as well too. We're starting a relationship with Microsoft, Azure, Google Compute Engine. So we've supported a variety of cloud expedients. We're starting a relationship with them and we work with some of the smaller players as well. Yeah, Michelle, as far as applications Sasha was talking about, if I got a pretty big portfolio and I'm talking about a pretty big migration, a big decision, how do I know what's going to work where? Can I stick my toe in the water a little bit or what can you do for people like me to allay those concerns that I know I'm going to work in a new environment? Yeah, it's one of the larger customers that we're working with is a large electricity company and they have 2,000 applications. They are trying to figure out exactly that challenge. What's going to work? What can I lift and shift? What has to be rewritten? One of the things that Velostrata can really help with is to allow them to test the waters, essentially. In five minutes, you can clone an application, try it in the cloud, zip it up to Amazon, test it, see if it's going to work. We automatically adapt and insert all the drivers and everything that's needed to adapt that application for the cloud so they can really get a sense of what the performance and cost is going to look like. So 2,000 apps though, so how do you prioritize that?  Right, so that takes some great consulting work for sure on the initial part, but the other thing is that the tools are getting better so that there's the analysis of figuring out what's going to work and what's not can take a lot less time. Yeah, I was going to just add on to that. We have a thing called discovery and analysis where you can go into that existing environment, get a lay of the land and you get all the dependencies of all those applications are tied together and then you can prioritize and group them as to how you move them. And again, she's right. It's not a matter of the old days of migration where you just move and you hope it works. You can now test it out before you turn off your current site before you actually move into the cloud. Yeah, bring up a great point. How much of what you're doing is software? How much of what you're doing is services today? Most of our stuff is software. The only reason we do services is if they're, do not have enough personnel to be able to operate the tool. The other thing is a lot of people are new to cloud. So we often do a lot of that education, whether it's vCloud Air from VMware, Softlayer, CenturyLink. We teach them what the best practices are for the cloud. So we augmented, but we're a software company. Yeah, Michelle? I would definitely agree. I mean, for us, obviously we're only a software company. We do some services analysis on the front end to help customers and figure out which applications are going to be their top priority. Okay, I'm curious. Coming to a show like this, you know, the developer angle sometimes is, well, we've got a lot of operators here. We really have a lot of administrators. Even when I talk about cloud, it's usually not kind of their number one or two skill set. Where are we with really the adoption of solutions like yours? How much education are you having to do? Pat Gelsinger talked about kind of this five year journey that we're going to see the next five years to public cloud. What's the state of the customer base? It depends on the company for sure. I think at this particular show, we see a lot of companies that are really trying to figure out what do I have today and then how do I figure out this cloud thing going forward? I think they've made a lot of progress around private clouds. So the virtualization piece of it is well understood, but the introduction of things like containers and again, moving applications to public cloud is a lot more challenging. I think we've come a long way. I mean, four years ago, we were at a retailer and I talked to an IT architect. He said, we're scared of the cloud. We don't want to lose our jobs, you know? And there were server huggers. And I think we've come a long way where people are realizing it's not about rack and stack. It's about how do I help my application developers? How do I get them to speed up their cycle so we can get a competitive edge in our business? So I think the adoption cycle is underway. We see large, even conservative clients. We have a big financial services company that we're going to be announcing soon. Very conservative, moving all of test dev to the cloud. All of it, so. So, I wonder if you can comment. There's three things that are usually kind of holding us back in some of this movement. There's the networking, just Amazon, Polsomston, security of course, major concern. And other operations, speak to, how's the maturity of those things? How does that impact what you're doing? Right, I mean, I think security used to come up and I'm sure you've experienced this. You know, four years ago, that was the reason no one wanted to go to the cloud. I think several things have happened. A lot of the cloud providers have improved security. It's new technology, it's new equipment. The thing is, data centers have old equipment, older software, that means there's security holes. That's more insecure than some of the clouds. As far as management, I think when VMware talks about hybrid, you can extend vCenter and do a lot of those things. I think the management kind of goes away. So I think a lot of those issues are being dealt with, management, security, and the risk that there is. Yeah, so just a quick follow-up on security. Sure, a few years ago, it was, oh, I'm not sure if the public cloud is secure. I do think we're past that. Do I have to have a security policy and ways of doing security that can actually live with my application wherever it is? We had a good chat conversation with Steve Herad, who's now a VC, former CTO of VMware. And that's where he's been spending a lot of it investing. So it's not just, oh, I'm going to trust Amazon or I'm going to do my own thing. I need to have something that can live anywhere. You really absolutely need to have something that lives anywhere. And you have to have security policies. Again, we're going back to this financial services company. The level of security that they live with, day in and day out, is amazing. But they've been able to translate those policies to the cloud, to particularly software. So I think it's important that you manage that. Of course you have technologies, we encrypt, we do data at rest, all of those things, the channel, the network has to be encrypted. You also mentioned network, that's a huge issue. So I think one of the things that we bring to the tables, we can help you more efficiently manage that network because you never have enough network bandwidth available to you. I think that's going to be important. I think on the networking topic to just build on that, I mean that's one of the exciting parts of the keynote announcement was this ability to transition the network to the cloud because that solves a huge percentage of that hybrid problem. I think organizations are going to take a while before they figure out how to tile those pieces together. What we see a lot of in our business is the concern about shadow IT and that because the cloud has made it so easy to spin up instances that IT starts to lose control over what workloads are being run in the cloud. And so there's a real opportunity for IT to really get back in the game there and take control over it. So she touched on a point a little bit ago that I think is, it's a pretty big consideration some people currently in the pipeline, they don't want to hear about cloud and they're worried about it because it's like, that's my job. I mean, how do you each deal with that? Because that is not a small consideration, big factor because you're dealing with people who have to make decisions that they find to be threatening to a certain degree. And that's absolutely what we dealt with in 2012 and 13. I think the market's obviously helped in doing the education is that there's going to be no options. People aren't going to spend millions of dollars on building data centers and all of that equipment. What we've been able to do to help that is working with the operators and training on the cloud. So you can translate those skills you currently have in your data center to the cloud so you're as valuable. Also to show them, making sure that your applications work and that you're really providing services to your users that's going to be much more critical than building more data centers and knowing how to operate a server. That's going to be a critical skill set in living into the future. What we've done from a technology standpoint to simplify that process is we've integrated everything into vCenter from a management standpoint. So they're using the tools they already know. It's literally a matter of right clicking on your VM and saying running cloud. So they don't need to learn the Amazon interface in order to make that happen. And before we let you all go, your takeaway from this week and what you want your lead behind to be as well about Rackware and Enneville Astrada. So what have you seen here big picture wise that you're going to take back and then what do you want people to know about your respective organizations? I mean, what I'm taking away is I think, you know, talking hybrid, it's now when VMware says it, it's market validation.  So we feel validation walking away from this and we also want enterprise clients to know there's solutions out there to say, you can believe in hybrid, you can go anywhere, you're not locked into your data center, you're not locked into Amazon and you're not locked into VMware either. You know, you can go anywhere and that's really important. That's our, I guess our leap behind. Yeah, I would absolutely agree. I think compared to VMware last year, VMware world last year, we've seen a pretty significant leap in adoption for public cloud and that's obviously encouraging. We believe that a number of the reasons and the challenges that companies have faced around risk, around data gravity have, you know, there's tools and technologies now that can help overcome those. So that's really exciting to see in terms of, you know, what we'll do with this information going forward. You know, we were really excited for this year. You know, we're seeing a tremendous jump in our business.  All right, well, thank you both for taking the time to be with us. Hope it's been a good week for you. It sounds like it's been very productive on a number of fronts and wish you continued success down the road. Thanks. Thank you for having us. Yeah, absolutely.  The Cube and our coverage of VMware will continue us here from Las Vegas in just a bit.


Hello, Myself, MS Bhasaragam, Assistant Professor, Department of Humanity Design Sciences, Valterist of Technology, Solapur. In this video, we are going to discuss about beta function part 1. Now, learning outcome. At the end of this session, students will be able to evaluate definite integral by beta function. Now, we will see what is beta function. Beta function beta of mn is defined by it is a function of m and n and it is denoted by b of mn. Therefore, beta of mn that is b of mn is equal to integration from 0 to 1 x raise to m minus 1 into bracket 1 minus x raise to n minus 1 dx, where m is greater than 0 and n is greater than 0. The beta function is also known as Euler's integral of first kind, it is a special kind of definite integral. For example, integration from 0 to 1 x square into bracket 1 minus x raise to 1 by 2 dx. Now, here we can compare this integral with the definition of beta function. Here, m minus 1 is 2 and n minus 1 is 1 by 2. Therefore, without integrating we can write the value of this integral as a function of that is beta of 3 and 3 by 2 that is here m is 3 and n is 3 by 2. Now, we will see important properties of beta function, first property is symmetric property beta of mn is equal to beta of nm that is if you interchange m and n the value of the given integral remains same. Now, next very important property is relation between beta and gamma function that is beta of mn is equal to gamma of m into gamma of n divided by gamma of m plus n that is here first of all we have to write the value of the integral in terms of beta function and we have to use the relation between beta and gamma function and we have to express beta in terms of gamma function and making use of the property of gamma function we can write the value of the given integral which is function of beta of mn. Now, we will see the example evaluate the integral integration from 0 to 2 x square into bracket 2 minus x raise to minus 1 by 2 dx. Now, to express this in terms of beta function here we have to bring the term 1 minus x for that the proper substitution is x is equal to 2 t that is dx is equal to 2 d t. Now, here accordingly we have to change the limits when x is equal to 0 we put x equal to 0 we get the value of t as a 0 and when x is equal to 2 we get the value of t is equal to 1. Therefore, the given integral integration from 0 to 2 x square into bracket 2 minus x raise to minus 1 by 2 dx is equal to integration from 0 to 1. Now, here putting x equal to 2 t that is you get 2 t whole square and putting x equal to 2 t then you get 2 minus 2 t raise to minus 1 by 2 and the value of dx as a 2 d t which is equal to here 2 raise to 2 and 2 that is 2 raise to 3 and taking 2 comma from this bracket that is 2 raise to minus of which simplifies which is equal to 2 raise to 5 by 2 integration from 0 to 1 we get t square into bracket 1 minus t raise to minus 1 by 2 d t. Now, which is in terms of beta function if you compare here m minus 1 is 2 and n minus 1 is minus 1 by 2 that we can write in terms of beta function which is equal to 2 raise to 5 by 2 beta of 3 and 1 by 2. Now, here using the relation between beta and gamma function we can write 2 raise to 5 by 2 as it is gamma of 3 into gamma of 1 by 2 divided by gamma of 3 plus 1 by 2 since we know just now we have seen beta of m n equal to gamma of m into gamma of n divided by gamma of m plus n which is equal to 2 raise to 5 by 2 into gamma of 3 into gamma of 1 by 2 divided by sum of this is what 7 by 2 that is what gamma of 7 by 2 which is equal to 2 raise to 5 by 2 and gamma of 3 can be written as 2 factorial that we know gamma of n plus 1 is n factorial keeping gamma of 1 by 2 as it is and here by using the reduction formula of gamma function gamma of 7 by 2 can be written as 5 by 2 into 3 by 2 into 1 by 2 into gamma of 1 by 2. Now, here gamma of 1 by 2 gamma of 1 by 2 will get cancel which is equal to 2 raise to 5 by 2 and this 2 into 2 into 2 that is we get 2 raise to 4 divided by 15 which is equal to we can write simplifying 2 raise to 6 root 2 divided by 15 that which is equal to we can write 64 root 2 by 15 this is what the value of the given integral pause the video for a while and find the value of beta of 5 by 2 3 by 2 I hope you have completed. Now, here we can write beta of 5 by 2 3 by 2 is equal to gamma of 5 by 2 gamma of 3 by 2 divided by gamma of 5 by 2 plus 3 by 2 since we know beta of m n is equal to gamma of m into gamma of n divided by gamma of m plus n. Now, simplifying this which is equal to we can write gamma of 5 by 2 can be written as 3 by 2 into 1 by 2 into gamma of 1 by 2 and gamma of 3 by 2 can be written as 1 by 2 into gamma of 1 by 2 and gamma of 5 by 2 plus 3 by 2 is gamma of 4 by simplifying we get which is equal to 3 by 8 gamma of 1 by 2 whole square and gamma of 4 can be written as 3 factorial which is equal to 3 by 8 and gamma of 1 half is root pi that is root pi whole square divided by 3 factorial means 3 into 2 into 1 that is 3 3 we get cancel which is equal to get pi by 16 which is what the value of beta of 5 by 2 and 3 by 2. Now, we will see the next example evaluate the integral integration from 0 to 2 x raise to 7 into bracket 16 minus x raise to 4 bracket raise to 10 dx. Now, here we have to express this integral in the form of beta function that is integration from 0 to 1 x raise to m minus 1 into 1 minus x raise to n minus 1 dx form for that here the suitable substitution is we have to make use here is x raise to 4 we have to substitute here x raise to 4 equal to 16 t that is solving for x we get x equal to 2 into t raise to 1 by 4. Therefore, dx is equal to 2 into 1 by 4 t raise to minus 3 by 4 dt that is dx is equal to 1 by 2 t raise to minus 3 by 4 dt. Now, according to the substitution you have to change the limits when x is equal to 0 what you get here t equal to 0 and when if you substitute x equal to 2 2 2 will get cancel you get the value of t will be 1. Therefore, the given integral integration from 0 to 2 x raise to 7 16 minus x raise to 4 raise to 10 dx is equal to now here limit will become integration from 0 to 1. Now, here we are substituting x equal to 2 t raise to 1 by 4 that is 2 raise to 7 t raise to 1 by 4 raise to 7 into bracket 16 minus 16 t raise to the bracket 10 and the value of dx as 1 by 2 t raise to minus 3 by 4 dt. Now, which is equal to here 2 raise to 7 divided by 2 means what we get 2 raise to 6 and from this bracket taking 16 common we get 16 raise to 10 integration from 0 to 1 and t raise to 7 by 4 and t raise to minus 3 by 4 means t into bracket 1 minus t bracket complete raise to the power 10 dt which is equal to 2 raise to 6 into 16 raise to 10 can be written as 4 into 16 raise to 11 and now comparing with definition of beta function here m minus 1 is 1 and n minus 1 is 10 therefore, you get m equal to 2 and n equal to 11 which is equal to 4 into 16 raise to 11 into beta of 2 11. Now, again here using the relation between beta and gamma function you get 4 into 16 raise to 11 into gamma of 2 into gamma of 11 divided by gamma of 13. Now, further by using the property of gamma function you can write which is equal to 4 into 16 raise to 11 into gamma of 2 can be written as 1 factorial, gamma of 11 can be written as 10 factorial, gamma of 13 can be written as 12 factorial which is equal to 4 into 16 raise to 11 1 factorial is 1 keeping 10 factorial as it is and writing 12 factorial as 12 into 11 into 10 factorial. Now, here 10 factorial 10 factorial will get cancel which is equal to 16 raise to 11 by 33 which is the value of the given definite integral. Now, you will see one more simple example express in terms of beta function integration from 0 to 1 square root of 1 minus x raise to 4 dx. Now, to get this integral in the form of beta function here power power substitution is you have to make use of x raise to 4 equal to t. Now, solving for x you get x equal to t raise to 1 by 4 that is dx is equal to 1 by 4 t raise to minus 3 by 4 dt. Now, according to the substitution you have to change the limits. Now, when x is equal to 0 you get t equal to 0 and when x is equal to 1 you get t equal to 1. Therefore, the given integral integration from 0 to 1 square root of 1 minus x raise to 4 dx is equal to integration from 0 to 1 1 minus t raise to 1 by 2 and the value of dx as 1 by 4 t raise to minus 3 by 4 dt taking 1 by 4 outside which is equal to 1 by 4 integration from 0 to 1 t raise to minus 3 by 4 into bracket 1 minus t raise to 1 by 2 dt. Now, we express this in terms of beta function and we can write the value of this integral in terms of beta function as which is equal to 1 by 4 as it is beta of 1 by 4 comma 3 by 2. This is what the value of the given integral in terms of beta function.