random variable X has a PDF f(x)=C(8*x−x^2) for 0

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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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A random variable X has a PDF f(x)=C(8*x−x^2) for 0<x<8, and is equal to 0 outside this range.

(a) Find the value of the constant C

(b) Find the CDF of  X and use it to compute the probability that X≥4

(c) Calculate the mean and variance of X

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