Question

Problem 4 Suppose X is a discrete random variable following distribution p(x), where x takes values in a discrete set. (1) Prove E(aX) = aE(X). (2) Prove E(X + b) = E(X) + b. (3) Prove Var(aX) = a^2Var(X). (4) Prove Var(X + b) = Var(X). (5) Prove Var(X) = E(X^2) - E(X)^2. (6) Let ? = E(X), and ?^2 = Var(X). Let Z = (X - ?)/?. Calculate E(Z) and Var(Z).

Name: Problem 4 Suppose X is a discrete random variable following distribution p(x), where x takes values in a discrete set. (1) Prove E(aX) = aE(X). (2) Prove E(X + b) = E(X) + b. (3) Prove Var(aX) = a^2Var(X). (4) Prove Var(X + b) = Var(X). (5) Prove Var(X) = E(X^2) - E(X)^2. (6) Let ? = E(X), and ?^2 = Var(X). Let Z = (X - ?)/?. Calculate E(Z) and Var(Z).
Uploaded: 2023-03-12T04:23:38-08:00
Duration: 1 min 56 s
Channel: Sri K
Description: Problem 4 Suppose X is a discrete random variable following distribution p(x), where x takes values in a discrete set. (1) Prove E(aX) = aE(X). (2) Prove E(X + b) = E(X) + b. (3) Prove Var(aX) = a^2Var(X). (4) Prove Var(X + b) = Var(X). (5) Prove Var(X) = E(X^2) - E(X)^2. (6) Let ? = E(X), and ?^2 = Var(X). Let Z = (X - ?)/?. Calculate E(Z) and Var(Z).

          Problem 4 Suppose X is a discrete random variable following distribution p(x), where x takes values in a discrete set. (1) Prove E(aX) = aE(X). (2) Prove E(X + b) = E(X) + b. (3) Prove Var(aX) = a^2Var(X). (4) Prove Var(X + b) = Var(X). (5) Prove Var(X) = E(X^2) - E(X)^2. (6) Let ? = E(X), and ?^2 = Var(X). Let Z = (X - ?)/?. Calculate E(Z) and Var(Z).

Problem 4 Suppose X is a discrete random variable following distribution p(x), where x takes values in a discrete set. (1) Prove E(aX) = aE(X). (2) Prove E(X + b) = E(X) + b. (3) Prove Var(aX) = a^2Var(X). (4) Prove Var(X + b) = Var(X). (5) Prove Var(X) = E(X^2) - E(X)^2. (6) Let ? = E(X), and ?^2 = Var(X). Let Z = (X - ?)/?. Calculate E(Z) and Var(Z).

Added by Shannon P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

03/12/2023

Step 1

Prove E(aX) = aE(X) E(aX) = ∑(a * x * p(x)) = a * ∑(x * p(x)) = a * E(X) So, we have proved that E(aX) = aE(X). Show more…

Show all steps

Thanks for your feedback!

Suppose X is a discrete random variable following distribution p(x), where x takes values in a discrete set. (1) Prove E(aX) = aE(X). (2) Prove E(X + b) = E(X) + b. (3) Prove Var(aX) = a^2Var(X). (4) Prove Var(X + b) = Var(X). (5) Prove Var(X) = E(X^2) - E(X)^2. (6) Let μ = E(X), and σ^2 = Var(X). Let Z = (X - μ)/σ. Calculate E(Z) and Var(Z).