Problem 2STE

Suppose that X takes on one of the values 0, 1, and 2. If for some constant c,P{X = i} = cP{X = i− 1}, i = 1, 2, find E[X].

Answer

Step 1 of 1

(a)

Suppose that takes on one of the values If for some constant

We are asked to find

We have given

This relationship implies that where

Because these probabilities sum to 1, we can write,

We know the expectation of a random variable

Hence is