Question

Let X be a random variable uniformly distributed on [-1, 1]. - What is E[X] and Var(X)? - What is E[X^2] and Var(X^2)? - Suppose we pick m numbers X1, X2, ..., Xm, where each is independent and each is uniform on [-1, 1]. Let Z = X1^2 + X2^2 + X3^2 + Xm^2. What is the expected value of Z? What is the standard deviation?

Name: let x be a random variable uniformly distributed on 1 1 what is ex and varx what is ex2 and varx2 suppose we pick m numbers x1 x2 xm where each is independent and each is uniform on 1 1 let 82748
Uploaded: 2022-04-26T08:54:10-08:00
Duration: 3 min 47 s
Channel: Shaiju T
Description: let x be a random variable uniformly distributed on 1 1 what is ex and varx what is ex2 and varx2 suppose we pick m numbers x1 x2 xm where each is independent and each is uniform on 1 1 let 82748

          Let X be a random variable uniformly distributed on [-1, 1].
- What is E[X] and Var(X)?
- What is E[X^2] and Var(X^2)?
- Suppose we pick m numbers X1, X2, ..., Xm, where each is independent and each is uniform on [-1, 1]. Let Z = X1^2 + X2^2 + X3^2 + Xm^2. What is the expected value of Z? What is the standard deviation?

Added by Michael P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shaiju T

04/26/2022

Step 1

Therefore, E[X] = 0. The variance of a uniform distribution on [-1, 1] is given by Var(X) = (1 - (-1))^2 / 12 = 1/3. Show more…

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Let X be a random variable uniformly distributed on [-1, 1]. - What is E[X] and Var(X)? - What is E[X^2] and Var(X^2)? - Suppose we pick m numbers X1, X2, ..., Xm, where each is independent and each is uniform on [-1, 1]. Let Z = X1^2 + X2^2 + X3^2 + Xm^2. What is the expected value of Z? What is the standard deviation?