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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Two coins refresher
Given a world that consist of bunch random events (2 coins for simplicity) we are interested in quantifying the probability of different combinations of the world state.
The state space
The combination of all possible outcomes is called the state space $\Omega$, in our example 
Coin 1 | Coin 2
-------------|-------------
H | H
H | T
T | H
T | T
An event is a subset of the state space, denoted as $A \subseteq \Omega$, the following are examples of events
E1
Step1:  Probability is amazing - Computing integrals
Step2:  Your turn
Compute the area of the normal distribution between [-3, 3]
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Python Code:
#Your code here
Explanation: Two coins refresher
Given a world that consist of bunch random events (2 coins for simplicity) we are interested in quantifying the probability of different combinations of the world state.
The state space
The combination of all possible outcomes is called the state space $\Omega$, in our example 
Coin 1 | Coin 2
-------------|-------------
H | H
H | T
T | H
T | T
An event is a subset of the state space, denoted as $A \subseteq \Omega$, the following are examples of events
E1: Exactly one head occurs or {HT, TH}
E2: Exactly one tail occurs or {HT, TH}
Proababilty
The probability measure is a function $P: \mathbb{R}\rightarrow[0,1]$ that satisfies 3 axioms
- $P(A) >= 0$, $\forall A \subseteq \Omega$
- $P(\Omega) = 0$
- for disjoint $A1, A2$  $P(A1, A2) = P(A1) + P(A2)$
Our understanding of probability
Frequentist interpretation
The probability is the fraction of the event occurrence to number of trials
$P(X=x) = \lim_{N\rightarrow \infty}\frac{n_x}{N}.$
Bayesian interpretation
The probability represents our belief that some event will occur (examples later)
Some rules
if we have two events $A$ and $B$ 
- $P(A, B)$ is called the Joint probability
- $P(A)$ is the Marginal probability and  can be computed by $\sum_{B} P(A, B)$
- $P(A|B)$ is the Conditional probability and can be cumputed by $\frac{P(A, B)}{P(B)}$
- $A$ and $B$ are independent if $P(A|B) = P(A)$
- If A and B are independent then $P(A, B) = P(A)P(B)$
Problem
Given the three fair coins find the follwing 
The state space 
P(C1 = H)
P(C1 = H, C2 = T)
Check that C1 is H and C2 is H are independent
End of explanation
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
radius = 1
N = 10000
X = np.random.uniform(low=-radius, high=radius, size=N)  # Random numbers from -1 to 1
Y = np.random.uniform(low=-radius, high=radius, size=N)   
is_point_inside = np.sqrt(X**2 + Y**2) < radius
plt.scatter(X,Y, c=is_point_inside, s=5.0, edgecolors='none', cmap=plt.cm.Accent)  
plt.axis('equal')
p_inside = np.sum(is_point_inside) / N
circle_area = box_area * p_inside
print ("Area of the circle = ", circle_area)
print ("pi = ", circle_area/radius**2)
Explanation: Probability is amazing - Computing integrals
End of explanation
#Your code here
Explanation: Your turn
Compute the area of the normal distribution between [-3, 3]
End of explanation
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