40 Let f(x) be any pdf with mean μ and variance o2. Show how to create a location-scale family based on f(x) such that the standard pdf of the family, say f*(x), has mean 0 and variance 1. 41 A family of cdfs {F(x0), 0 0} is stochastically increasing in 0 if 0₁ > 02 ⇒ F(x|0₁) is stochastically greater than F(x|02). (See Exercise 1.49 for the definition of stochas- tically greater.)

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Q: 3. Suppose that X is a continuous random variable with pdf 32², 0<x< 1 0, otherwise Let Y= 2X + 3.…

A: f(x)=3x2; 0&lt;x&lt;1

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Q: Question 5 Let X1 and X2 be random sample of normal distribution with mean 1 and 2 and variance 3…

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Q: Suppose that { Y,} is Moving average process with Y, = 0.25(e, + e,-1+e-2+ej_3) %3D where {e,} is…

A: Find Mean, variance, auto covariance function and auto correlation function

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A: Given  Xt=Wt+12Wt-1+13Wt-2 where Wt=WNσ2=1

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Q: Q4) Assume that a variable x comes from a probability distribution of the form P(x|w) exp(Σwkf(x) 1…

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Q: i) Find the cumulative distribution function (CDF) of X. 8 ii) Show that the moment generating…

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Q: Let X and Y be identically distributed with mean 4 and variance 25.(a) If X and Y are uncorrelated,…

A: a) If X and Y are uncorrelated then Cov(X,Y)=0, given V(X)=V(Y)=25 Answer(a): 50

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Q: Let X₁, X₂,..., Xn be a random sample from an exponential distribution with the pdf e-/, for 0 < x…

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Q: (6) Let X be a Poisson random variable with parameter 9, then E(X²) = 1.

A: Given X~Pois(θ)

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Q: (c) Compute the variance of X using its MGF.

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Q: Question 6. Suppose that Y has the pdf fy(u) = 1, 0 < <1, zero elsewhere. Let X =-7 In(Y). Then, the…

A: The cumulative distribution function is defined as F(x) = P(X ≤ x)

Q: False

A: Random Process: A random process is a stochastic process. It is denoted by X(t) that is the value of…

Q: (1) Let X = b(16,) find E(4-3x) and distribution function.

A: From the provided information, X~b (16, 1/4) Sample size (n) = 16 Probability (p) = 1/4

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Q: The continuous random variable X has the pdf f(x) = { (a) Find the cdf F of X. if x < 1 -2 (x-² if x…

A: Let X be a continuous random variable with the pdf given f(x),f(x)={0if x&lt;1x−2if x≥1To find:a)…

Q: (1) Let X b(16, find E(4-3x) and distribution function.

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Q: 5. Find the moment generating function of the exponentially distributed random vari- able with pdf…

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Q: Example 2.17 Let X be a continuous type random variable with PDF given as f(x) = 27 Let Y be another…

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Q: Example 2.7. Let X and Y be jointly continuous random variables with joint PDF is given by: fx,y (r,…

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Q: Use the moment-generating function of gamma distribution to show that E(X)=a0 and Var(X)=a®² ||

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