(b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If yes, give a proof; if no, give a counterexample.

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A: Moment generating function:

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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: Two random variables X andY are independent if f(x, y) = f1(x). f2(y) Select one: O True O False

A:

Q: Select one: а. О b. 2 C. var(x) d. - 2 e. 1

A: To find the value E[X(1-X)].

Q: If the moment generating function of a random variable X is: (1/3+(2/3)e t ) 5 find P (X > 3).

A: The given moment generating function of a random variable X is 13+23et5.

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A:

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

Q: E(Y) –> P(Y > n).

A:

Q: Find the value of the constant c. Find P(YX). Find P(Y = X).

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Q: If X is a random variable, prove that Cov(X,X) = σX².

A: Let X is a random variable.

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Q: (a) Compute E(XY). (b) Compute E(X).

A:

Q: Suppose that Y is a continuous random variable. Show EY = yfr(y)dy.

A: Here, we have to prove EY=∫-∞∞yfydy.

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A: Let X be random variable with pdf

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A: Option (I) is correct as E(X2)>= (E(X))2 when we find Variance.

Q: Let Y be the Exponential random variable withl > 0. Find the following probabilities. 1(1 3(1

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

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A: The logically random variable we mean a real number X associated with the outcomes of a random…

Q: (b) Let Z be a discrete random variable with E(Z) = 0. Does it necessarily follow that E(Z³) = 0? If…

A:

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Q: ). Let M = ln(5*X) be a derived random variable. What is E[M]?

A:

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A: For the random variable X~Exponential1λ, it is given that: fx=1λe-xλ, for x≥0

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A: The joint probability distribution of the random variables is given as follows:

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Q: prove that var (XY) == 0} 03+ 2} · o3+ 13.03

A:

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A:

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A: Let  X be a random variable with the pdf  fx=2e-2x                 0&lt;x&lt;∞0…

Q: Suppose that X is a random variable for which E(X) = μ and Var(X) = σ2. Show that E[X(X − 1)] = μ(μ…

A:

Q: Let Z be a discrete random variable withE(Z)=0. Does it necessarily follow that E(Z3)=0? If yes,…

A: Solution

Q: Let X be a continuous random variable with pdf f(x) = x² for -1 < x < c. Find the value of c.

A: From the given information, the pdf of the random variable X is,

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: