11. Let X be a random variable with the following probability distribution: t X f(x) -3 6 2 9 T 3 Find E(X) and E(X²) and then, using these values, evaluate E[(2X + 1)²].

Q: If X is a random variable with probability distribution shown below, find E(X). x Pr[X-x] -2 0.1 0…

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Q: For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))

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

Q: Suppose that we have a discrete random variable Xa with PDF and CDF fa(x) and Fa(x), and a…

A: Explain the concept of mixed random variables. Let Y be a discrete random variable , Z be a…

Q: Exercise 3. Let X be a random variable with mean µ and variance o². For a E R, consider the…

A: Farmula used  V(X)=E(X2)-[E(X)]2

Q: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

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Q: Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

A: Given that X follows Uniform (a,b)  We have to find E(X) , Variance and E(X2)-E(X)

Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…

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Q: et X be a discrete random variable with P(X = -2) = .1, P(X = 1) = .15, P(X = 2) = .4, P(X = 4) =…

A:

Q: Let X denote a random variable that takes on any of the values -1, 0, 1 with respective…

A: P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3.

Q: let Y be a random variable that can either be equal to 0 to 1. let p(Y=1)=p,what is E(|Y-p|)?

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Q: 1. Let X1, X2, X3 be identically distributed independent exponential random variables and Y = X₁+ X2…

A: Given that X​1, X2​, and X3​ are identically distributed independent exponential random variables…

Q: Let X be a random variable having p.d.f. fx(x) = cx², -2 < x < 2. For the following parts, your…

A: Given density function: fx=cx2, -2&lt;x&lt;2 c value: ∫-22fxdx=1 from the total probability…

Q: Let X be a random variable with the probability distribution below. Find g(x), where g(x) = (2x +…

A: Given datax          -3        6         9f(x)       512      112      12andg(x)=(2x+3)2

Q: Suppose that the random variables Y and X only take the values 0 and 1, and have the following joint…

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Q: a) Write E((X − a)²) in terms of a, μ and oʻ. b) For which value a is E((X − a)²) minimal? c) For…

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Q: B5. Let X₁, X2,..., Xn be IID random variable with common expectation and common variance o², and…

A: Let X1, X2, . . . ., Xn be i.i.d. random variable with a common expectation E(Xi)=μ and common…