4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the following statements are true? • (i) E(1+ X*) >1+(E(X))'. (ii) E(|X|) > |E(X)|- • (iii) E(e!3X) > el3E(X).

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A: Solution

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A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

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A: It is given that X is a discrete random variable with finite first and second moment.

Q: 9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution…

A:

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Q: 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties…

A: Given,E(X)=15Var(X)=10and Y=2X-7

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A: 1] Var(Z)=12 2] E(Z)=2

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A:

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A:

Q: 1. Let X be a Poisson random variable with parameter A. Derive E(X) and E(2x)

A:

Q: Suppose X is a continuous random variable with probability dens function 0.3 0 1 What is the…

A: The variable X is a continuous random variable.

Q: Let us say that we have jointly distributed random variables X and Y with E(X) = 3, E(Y) = 5, Var…

A:

Q: X and Y be two discrete random variables with a joint p en by X-0 X-2 Y=1 0.03 0.02

A: to find P(X&gt;0 and Y≤3)

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A: The given dF is : F(x)=0for x≤01-exfor x&gt;0 We want to find quantile function.

Q: 2. Suppose that X is a standard uniform random variable and Y|X = x ~Normal(x,x) for 0 ≤ x ≤ 1. Find…

A: Solution (2) There is two different questions So i am solving first

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A:

Q: , Let X1, X2, ,X, be a sequence of i.i.d. Bernoulli(p) random variables and let Y, = E X/n. Show…

A:

Q: 1. For any random variable X for which E(X) and E(X²) are finite, show that Var(X) = E(X²) – [E(X)]²…

A:

Q: 1. Show that if X' , Y' are the deviations of the random variables X and Y from their respective…

A: Given that, Xi' and Yi'are the deviations of random variables X and Y form their means. Xi' = Xi-X¯…

Q: Consider a random sample X1, X2, ..., X, from Bernoulli's distribu- tion B(1, p). Prove that X; is a…

A:

Q: A continuous random variable has a p.d.f. ſkx³(1 – x)²0 < x < 1 | f(x) = Ootherwise

A: Given,f(x)={kx3(1-x)2  ;0&lt;x&lt;10                   ;otherwise

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Q: what is E[XY]?

A:

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A:

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A:

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Q: 1. Let X, 2 Poisson(A,), for i = 1,2. (a) Show that X1 + X2~ Poisson(A1 + Ag). (b) Show that X| X +…

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Q: 10- If the random variable X has the gamma p. d. f with integer parameter a and arbitrary ß> 0, then…

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Q: (4) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x)= , find E(e2x) O.w

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A: Given function is f(x)={x6+k    0≤x≤30          elsewhere

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A: It is given that X is a random variable. Therefore, Bernoulli distribution is,

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Q: If X is a continuous random variable with distribution, f(x) =*+ k if 0 < x< 3 = 0 elsewhere…

A: if X is a continuous random variable with distribution,f(x)=x6+kif 0≤x≤30elesewhere

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A:

Q: 1. Given that x is a continuous random variable that is uniformly distributed in a range from 8 to…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 4.Suppose that X is a random variable for which E(X)=µ and Var(X)=o². Show that E(X(X-1)]=µ(µ-1)+o?

A: It is given that E(X) = μ and Var(X) = σ2

Q: For the random variables X,Y Cov(X,Y) = -0.9 if Z=3-X then what is Cov(Z,Y)=???

A: Given - Cov ( X , Y ) = -0.9 Z = 3-X