Question

Let X be a random variable that assumes values: 0,1,2,3 with corresponding probabilities of 1/6, 1/3,1/6 and 1/3 respectively. Find the following a) The expected value of g(x)=(X-2)^2 ; b) The variance of g(X) = (X-2)^2

Name: let x be a random variable that assumes values 0123 with corresponding probabilities of 16 1316 and 13 respectively find the following a the expected value of gxx 22 b the variance of gx x 2 81802
Uploaded: 2024-01-05T23:32:59-08:00
Duration: 3 min 41 s
Channel: Joanna Quigley
Description: let x be a random variable that assumes values 0123 with corresponding probabilities of 16 1316 and 13 respectively find the following a the expected value of gxx 22 b the variance of gx x 2 81802

          Let X be a random variable that assumes values: 0,1,2,3 with
corresponding probabilities of 1/6, 1/3,1/6 and 1/3 respectively.
Find the following a) The expected value of g(x)=(X-2)^2 ; b) The
variance of g(X) = (X-2)^2

Added by Patrick S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Joanna Quigley

01/05/2024

Step 1

E[g(X)] = E[(X-2)^2] = Σ[(x-2)^2 * P(X=x)] We have the values of X and their corresponding probabilities: x = 0, P(X=0) = 1/6 x = 1, P(X=1) = 1/3 x = 2, P(X=2) = 1/6 x = 3, P(X=3) = 1/3 Now, we can calculate E[g(X)]: E[g(X)] = (0-2)^2 * (1/6) + (1-2)^2 * Show more…

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Let X be a random variable that assumes values: 0,1,2,3 with corresponding probabilities of 1/6, 1/3,1/6 and 1/3 respectively. Find the following a) The expected value of g(x)=(X-2)^2 ; b) The variance of g(X) = (X-2)^2