Suppose that a random variable X has the following probability density function.SC(36-x²) 0 ≤ x ≤ 6otherwisef(x) = {C (²Find the expected value of X.(You will need to find the value of the constant C so that f is a pdf.)

Answered: Suppose that a random variable X has…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that a random variable X has the following probability density function.
SC(36-x²) 0 ≤ x ≤ 6
otherwise
f(x) = {C (²
Find the expected value of X.
(You will need to find the value of the constant C so that f is a pdf.)

Expert Solution

Step 1: Determine the given data

From the provided information,

$f open parentheses x close parentheses equals open curly brackets table row cell C open parentheses 36 minus x squared close parentheses end cell cell 0 less or equal than x less or equal than 6 end cell row 0 cell text otherwise end text end cell end table close$