Let X be a RV with PMF Px(x) = x²/c |0 x = −3, −2, −1, 0, 1, 2, 3, otherwise. (a) Find c and E[X]. (b) What is the PMF of the random variable Z = (X – E[X])²? (c) Using the results from (b), find the variance of X. (d) Find the variance of X using the formula var(X) = Σx(x − E[X])²px(x).
Let X be a RV with PMF Px(x) = x²/c |0 x = −3, −2, −1, 0, 1, 2, 3, otherwise. (a) Find c and E[X]. (b) What is the PMF of the random variable Z = (X – E[X])²? (c) Using the results from (b), find the variance of X. (d) Find the variance of X using the formula var(X) = Σx(x − E[X])²px(x).
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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![1. Let X be a RV with PMF
Px (x) =
=
[x²/c
X = −3,−2, –1, 0, 1, 2, 3,
otherwise.
(a) Find c and E[X].
(b) What is the PMF of the random variable Z = (X – E[X])²?
(c) Using the results from (b), find the variance of X.
(d) Find the variance of X using the formula var(X) = Σx(x − E[X])²px(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F230dd6fc-67da-4f36-8738-d9d162992241%2Fdbd9fd71-44c5-4448-81ca-979859da07cd%2Fbdhtb3c_processed.png&w=3840&q=75)
Transcribed Image Text:1. Let X be a RV with PMF
Px (x) =
=
[x²/c
X = −3,−2, –1, 0, 1, 2, 3,
otherwise.
(a) Find c and E[X].
(b) What is the PMF of the random variable Z = (X – E[X])²?
(c) Using the results from (b), find the variance of X.
(d) Find the variance of X using the formula var(X) = Σx(x − E[X])²px(x).
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