Answered: 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: PEARSON

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Question

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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

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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