Determine the mean and variance of the random

Chapter 4, Problem 40E

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QUESTION:

Determine the mean and variance of the random variable in Exercise 4-2.

4-2.(+) Suppose that \(f(x)=3\left(8 x-x^{2}\right) / 256\) for 0 < x <. Determine the following:

\(P(X<2)\)\(P(X<9)\)\(P(2<X<4)\)\(P(X>6)\)X such that \(P(X<x)=0.95\)

Equation transcription:

Text transcription:

f(x)=3(8 x-x^{2}) / 256

P(X<2)

P(X<9)

P(2<X<4)

P(X>6)

P(X<x)=0.95

Questions & Answers

QUESTION:

Determine the mean and variance of the random variable in Exercise 4-2.

4-2.(+) Suppose that \(f(x)=3\left(8 x-x^{2}\right) / 256\) for 0 < x <. Determine the following:

\(P(X<2)\)\(P(X<9)\)\(P(2<X<4)\)\(P(X>6)\)X such that \(P(X<x)=0.95\)

Equation transcription:

Text transcription:

f(x)=3(8 x-x^{2}) / 256

P(X<2)

P(X<9)

P(2<X<4)

P(X>6)

P(X<x)=0.95

ANSWER:

Solution

Step 1 of 2

We have to determine the mean and variance of the random variable

The given function is

Mean=

         =

         =

         =

         =

         =

         =4


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