Homepage › Solution manuals › Joseph Blitzstein › Introduction to Probability › Exercise 3.40

Exercise 3.40

Answers

(a)

X

and

Y

need not have the same PMF. For example, let

Y

represent my answer to the question, "What is the capital of Zimbabwe?" I believe it to be Harare with probability

\frac{3}{4}

, but I am not certain, so with probability

\frac{1}{4}

, I think it may be Bulawayo.

Tom on the other hand knows for a fact (probability of $1$ ) that the captial of Zimbabwe is Harare.

Suppose Tom gets asked first. I trust Tom, so I will always go with Tom’s answer once I hear it. Letting $X$ and $Y$ be my and Tom’s answers to the question, $P (X = Y) = 1$ , but the PMFs of $X$ and $Y$ are different.

(b)

P (X = Y) = 1

, then

X

and

Y

can not be independent, the outcome of one fixes the outcome of the other.

fifthist

2021-12-05 00:00

Exercise 3.40

Answers

Comments

Add answer