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4. This problem shows (more or less) that if X is a nonnegative random variable with E(X) = 0, then X = 0 with probability 1. (a) Show that if X is a random variable that only takes on nonnegative values, then E(X) > 0. You will likely need to give separate proofs depending on whether X is discrete or continuous. (b) Show that if X is a discrete random variable that only takes on nonnegative values and E(X) = 0, then P(X = 0) = 1. In other words, X must be constant. (c) (Extra credit) Show that if X is a continuous random variable that only takes on nonnegative values, then E(X) # 0 (problem 4 from HW6 is one way to approach this).

4. This problem shows (more or less) that if X is a nonnegative random variable with E(X) = 0, then X = 0 with probability 1. (a) Show that if X is a random variable that only takes on nonnegative values, then E(X) > 0. You will likely need to give separate proofs depending on whether X is discrete or continuous. (b) Show that if X is a discrete random variable that only takes on nonnegative values and E(X) = 0, then P(X = 0) = 1. In other words, X must be constant. (c) (Extra credit) Show that if X is a continuous random variable that only takes on nonnegative values, then E(X) # 0 (problem 4 from HW6 is one way to approach this).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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4. This problem shows (more or less) that if X is a nonnegative random variable with E(X) = 0, then X = 0 with probability 1. (a) Show that if X is a random variable that only takes on nonnegative values, then E(X) 20. You will likely need to give separate proofs depending on whether X is discrete or continuous. (b) Show that if X is a discrete random variable that only takes on nonnegative values and E(X) = 0, then P(X = 0) = 1. In other words, X must be constant. (c) (Extra credit) Show that if X is a continuous random variable that only takes on nonnegative values, then E(X) # 0 (problem 4 from HW6 is one way to approach this).
Transcribed Image Text:4. This problem shows (more or less) that if X is a nonnegative random variable with E(X) = 0, then X = 0 with probability 1. (a) Show that if X is a random variable that only takes on nonnegative values, then E(X) 20. You will likely need to give separate proofs depending on whether X is discrete or continuous. (b) Show that if X is a discrete random variable that only takes on nonnegative values and E(X) = 0, then P(X = 0) = 1. In other words, X must be constant. (c) (Extra credit) Show that if X is a continuous random variable that only takes on nonnegative values, then E(X) # 0 (problem 4 from HW6 is one way to approach this).
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