The random variable X has the following probability density function: 2x 0 ≤ x ≤ 3 9 f(x) = 0, otherwise (a) (3 points) Show that this is a valid PDF. (b) (3 points) Find the expected value E(X) of X. (c) (4 points) Find the variance Var(X) of X.

The random variable X has the following probability density function: 2x 0 ≤ x ≤ 3 9 f(x) = 0, otherwise (a) (3 points) Show that this is a valid PDF. (b) (3 points) Find the expected value E(X) of X. (c) (4 points) Find the variance Var(X) of 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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help me with abc please. please handwrite if possible. please don't use AI tools to answer.

The random variable X has the following probability density function:
2x
0 ≤ x ≤ 3
9
f(x) =
0,
otherwise
(a) (3 points) Show that this is a valid PDF.
(b) (3 points) Find the expected value E(X) of X.
(c) (4 points) Find the variance Var(X) of X.

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