Exercise 7. The probability that a coin has to land Heads is unknown, say p, where p is some number in [0,1]. Let X be a random variable that takes the value 1 if the coin lands Heads and 0 if the coin lands Tails. What is its expected value and standard deviation? Solution P(X = 1) = p P(X = 0) = 1 - P(X = 1) = 1 - p So the distribution of X is: P(X=0) = 1-p , P(X=1) = p expected vaule =xp(x)=1*p+0*(1-p) =p varaince=x2p(x)-2 =p2-p2 =0.

1. Exercise 7. The probability that a coin has to land Heads is unknown, say p, where p is some
number in [0,1]. Let X be a random variable that takes the value 1 if the coin lands Heads and 0
if the coin lands Tails. What is its expected value and standard deviation?
Solution
P(X = 1) = p
P(X = 0) = 1 - P(X = 1) = 1 - p
So the distribution of X is:
P(X=0) = 1-p , P(X=1) = p
expected vaule =xp(x)=1*p+0*(1-p)
=p
varaince=x2p(x)-2
=p2-p2
=0