For a random variable X, (E(X))² can be greater than E(X²).

Q: For the random variable X. E(X) = 2, E(X =7 then the value of Tar(2X+3) is

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Q: 1. determine the likelihood function L(x: 0) = f(x₁,x2,...,xn|0) and the maximum likelihood…

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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: P(X=0)=P(X=2)

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Q: Let X1, X2,... be independent Exponential (3) random variables and Z = } E=1 X;. If Mz (t) is the…

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Q: The continuous random variable X has a cumulative distribution function F(x) given by: x 2. Find…

A: The CDF of X is given by, Fx = 0x<1kx4+x2-21≤x≤21x>2 Now, X is continuous random variable. So,…

Q: If X,, X2,...,X, constitute a random sample of size n from a population with p.d.f. given by .....…

A: Find MLE of θ

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

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Q: Let the random variable X have the moment generating function e³t M(t) = 1-t²-1<t<1 What are the…

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Q: X³, 2Y²-3Y+4)  Calculate the covariance by creating a common distribution table for the given…

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Q: 3t For a random variable X with mgf Mx(t) = exp{t² – }; Find E[X²]

A: Given, MXt=expt2-3t2 Now, ddtMxt=ddtexpt2-3t2=expt2-3t2×ddtt2-3t2=expt2-3t2×2t-32=expt2-3t2×4t-32…

Q: For a certain random variable X it is known that E[X]=2, Var(X)=3. What E[x']?

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Q: The cumulative distribution function for a random variable X is given by: 1-e for x20 F(x)=-…

A: Given the cumulative distribution function for a random variable X as FX=1-e-2x           for   x⩾00…

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

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Q: Let X1, X2, ..., Xn be independent random variables and Y = min{X1, X2,..., Xn}. n Fy(y) = 1 – II (1…

A: Given that X1, X2, . . . , Xn be independent random variables and Y=minX1, X2, . . . , Xn…

Q: Let x be an exponentially distributed continuous random variable, with f(x) = ce¯«, for 0 < x < «,…

A: a) Consider,…

Q: A continuous random variable X is defined by: Solve: 1. f(x) = (3+x)²/16  ; -3≤ x≤ -1 2. f(x) =…

A: Given: Let X be a continuous random variable. Solving the following density functions. 1.…

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

A: Provided probability density function is, fx=2e-2x         for 0&lt;x&lt;∞=0…

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

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Q: Let X₁ and X₂ be independent exponential random variables, with parameters X₁ and 2, respectively.…

A: Given : X1 and X2 are two independent exponential random variables with parameter lambda1 and…

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…

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Q: Q2) A continuous random variable has PDF Kx²+2x+1, -25xs 3. Find K, P(x)>0, X. X¹ and ².

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Q: Two random variables X and Y have the joint characteristic function Pxr (@,, a, ) = exp(-20f -8a})…

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Q: 1 For a random variable X with mgf Mx(t) = (1–4)'/2 Find E[X²]

A: Given: The moment generating function of the random variable X is given as:…

Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25         σ2x=0.36         σ2y=0.49 Thus,

Q: For the random variable transformation Y=X*X, the value of the expectation of Y is equal to E[Y]

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Q: The pdf of a random variable X is given by = 20 fx(x) = 23x<5 Find the pdf of Y = 3X - 5.

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Q: Let X1, X2,..., Xn be independent exponential random variables with mean if. For example, E(X1)=0,…

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Q: what is E[XY]?

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Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: The continuous random variable X has a cumulative distribution function F(x) given by: x 2. Find…

A: The probability distribution function is the derivative of the cumulative distribution function.

Q: Let X be a random variable with p.d.f. 2e-2x f(x)=< 0<x<0 , find E(e2") O.w

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

Q: If Y is an exponential random variable with parameter , then μ = E(Y) = 8 and o² = V(Y) = 8². The…

A: We have given that Y is an exponential random variable with parameters beta then mean = E(Y) = β…

Q: Let X and Y be two independent exponential random variables. X ~

A: Given,  X and Y be two independent exponential random variables.                       X~exp(1) and…

Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: If the time taken to repair a personal computer is a random variable X whose p.d. f is given by · ,0…

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Q: Suppose X1, X2,..., X10 are independent random variables, Find P(X1+ X2 +...+ X10 < 25), assuming…

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

Q: The joint p.d.f of a two-dimensional random variables (x, y) is given by f(x,y) = kxe , 0 0 = 0 ,…

A: To find k, we need to apply total probability =1.

Q: Let X be a random variable with p.d.f. 2e-2x 0< x<00 f(x) = , find E(x). O.w

A: We know that, E(x)= integration |x X*f(x) dx

Q: . Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Here, we have,  E[X] = 0 P(-3&lt;X&lt;2) = 1/2  Now, P(-2&lt;X&lt;2) = 1/2 (Since, X cannot be…

Q: Example 10 : If X is a continuous random variable and Y = aX + b, prove that = a E(X) + b and V(Y) =…

A: It is given that Y=aX+b.

Q: If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y…

A: X1,X2,X3 are same from a Bernoulli distribution. Y=X1+2X2+X3 Let X1,X2,X3 are from Bernoullip.

Q: Suppose X is a random variable whose pdf is given by f(x) =k(4x-2x^2) 01)

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Q: For the discrete random variable X, P(X = 1) = p = 1– P(X = -1). Please find c so as to be E(c*) =…

A: The given equation is P(X = 1) = p = 1 – P(X = -1) and E(cX) = 1.

Q: Consider the random variable X such that E(X) = 3 and Var(X) = 2 if the random variable Z = 1+5X.…

A: Given information:Given that the mean and variance of the variable X is 3 and 2.That is, E(X) = 3…