Question

Problem 1 Let X be a discrete random variable which takes on values in {0, 1, ..., N}. Show that in that case, the expected value of X can be written as E(X) = sum_{n=0}^{N-1} P(X > n)

          Problem 1
Let X be a discrete random variable which takes on values in {0, 1, ..., N}. Show that in that case, the expected value of X can be written as
E(X) = sum_{n=0}^{N-1} P(X > n)

Added by Susan W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

03/27/2023

Step 1

In this case, we are given that X takes values only in {0,1,N}, so we can write: E(X) = P(X=0)*0 + P(X=1)*1 + P(X=N)*N Now, we need to find a way to express P(X=k) in terms of P(X>n) for some n. One way to do this is to use the complement rule: P(X=k) = 1 - Show more…

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Problem 1 Let X be a discrete random variable which takes on values in {0, 1, ..., N}. Show that in that case, the expected value of X can be written as E(X) = sum_{n=0}^{N-1} P(X > n)