6 Consider a Bernoulli random variable X such that P X 1

6. Consider a Bernoulli random variable, X , such that P (X = 1) = p and
P (X = 0) = (1 p). Calculate the expected value and variance of X.

pls give me step by step solution!!!

Solution

Note that

E(x) = Sum(x P(x)) = 1(p) + 0(1-p) = p

Also,

E(x^2) = Sum(x^2 P(X)) = 1^2 (p) + 0^2 (1-p) = p

Thus,

Var(x) = E(x^2) - E(x)^2 = p - p^2

Thus,

E(x) = expected value = p [answer]
Var(x) = p - p^2 [answer]