3. A function is defined as(0f(x) =2x+3180x < 22≤x≤4X>4Show that f(x) is a probability density function and find P(2 < X<3).

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Answered: 3. A function is defined as (0 f(x) =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)
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Show that the following are the probability density functions: fi(x) = e-*I(0,c0) (x) f2(x) = 2e¬*I(o,00) f(x) = (0 + 1)f1 (x) – Of2(x) 0 < 0 < 1
Let X will be continuous random variable with probability density function as below. f(x) = {4x , (0

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3. A function is defined as (0 f(x) = 2x+3 18 0 x < 2 2≤x≤4 X> 4 Show that f(x) is a probability density function and find P(2 < X<3).