Solution Found!
Let Y1, Y2, . . . , Yn be independent and identically
Chapter 6, Problem 37E(choose chapter or problem)
Problem 37E
Let Y1, Y2, . . . , Yn be independent and identically distributed random variables such that for 0 < p < 1, P(Yi = 1) = p and P(Yi = 0) = q = 1 − p. (Such random variables are called Bernoulli random variables.)
a Find the moment-generating function for the Bernoulli random variable Y1.
b Find the moment-generating function for W = Y1 + Y2 + ··· + Yn .
c What is the distribution of W ?
Questions & Answers
QUESTION:
Problem 37E
Let Y1, Y2, . . . , Yn be independent and identically distributed random variables such that for 0 < p < 1, P(Yi = 1) = p and P(Yi = 0) = q = 1 − p. (Such random variables are called Bernoulli random variables.)
a Find the moment-generating function for the Bernoulli random variable Y1.
b Find the moment-generating function for W = Y1 + Y2 + ··· + Yn .
c What is the distribution of W ?
ANSWER:
Solution:
Step 1 of 3:
Let , …, be independent and identically distributed random variables such that for 0<p<1, P(and P(
We have to find,
- The moment-generating function for the bernoulli random variable Y1.
- The moment- generating function for W= ++...+.
- The distribution of W.