Consider the CDF given below. Also, assume X is a random variable whose CDF is given by F(x), Calculate: (1) P (X ≤ // ) (1) P (0 < X < ¹) F(x) = {x+05 1 (1) 4/14 OB x<0 -0.5 0

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A: The solution is given below.Explanation:Given:Given the probability density function (pdf) for a…

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A: The moment generating function of x is given by: Mxs=EesX=13es+23e2s+0e3sMxs=13es+23e2s

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A: It is a fact of statistics. It is widely used.

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A:

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A: Here,fx=dfxdx=dcx-14dx=4cx-13                                    ;1&lt;x≤3   Now, find c using the…

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A: Solution

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A: (i) fx=dFxdx                                  for 1&lt;x≤3=dcx-14dx=cdx-14dx=4cx-14-1=4cx-13…

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A: Given that  Y ~ Uniform (1 , 11)

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Q: (a) P(2 < Xs 5), (b) P(3 < X s 7), and (c) P(X 2 6). *

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A: Given Information: f(x) = 130x2+4 x = -2, -1, 0 , 1 , 2

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A: When X~ Pois(λ) P(X=x)=e-λ λx/x!  ; X=0,1,2,3,.. result: r!=r(r-1)(r-2)..3x2x1

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Q: 3x (1+х) Q2. If f(x) = ; 0<x <2 denotes the pdf of a continuous random variable, find mean 14 and…

A: Mean = E(X) = ∫xf(x)dx Variance = E(X2) - E(X)2 Where ,   E(X2) = ∫x2f(x) dx