Let X be a Bernoulli rv with pmf as in Example 3.18.

Question

LLet X be a Bernoulli rv with pmf as in Example 3.18. a. Compute E(X2 ). b. Show that V(X) 5 p(1 2 p). c. Compute E(X79).

Answer (Expert Verified)

The Bernoulli distribution is a distribution whose random variable can  only take 0 or 1

  • The value of E(x2) is p
  • The value of V(x) is p(1 – p)
  • The value of E(x79) is p

How to compute E(x2)

The distribution is given as:

p(0) = 1 – p

p(1) = p

The expected value of x2, E(x2) is calculated as:

So, we have:

Evaluate the exponents

Multiply

Add

Hence, the value of E(x2) is p

How to compute V(x)

This is calculated as:

Start by calculating E(x) using:

So, we have:

Recall that:

So, we have:

Factor out p

Hence, the value of V(x) is p(1 – p)

How to compute E(x79)

The expected value of x79, E(x79) is calculated as:

So, we have:

Evaluate the exponents

Multiply

Add

Hence, the value of E(x79) is p

Leave a Comment