Given that X and Y are independent random variables and E(X) = 4, E(Y) - 7, Var(X) = 3. Var(Y) = 6. find Var(10X - 3Y).

Q: If the variances for independent random variables X and Y is Var(X)=0.15 and Var(Y)=5.62 then Var…

A: Given that  Var(X)=0.15 Var(Y)=5.62

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: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

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: The profit for a new product is given by Z= 3X- Y- 5. If X and Y are independent random variables…

A: Answer - Given, Z = 3X - Y - 5             X and Y are independent random variables  with σx = 1…

Q: If X and Y are two random variables, then the covariance is Cxy = Ryy – XY

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Q: If the random variable X and Y have the joint probability distribution f(x, y) = x+y, 0<x< 1,0 <y<1…

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Q: 1) If Var(X-Y) = 2, Var(X+Y) = 4, E(X) = 3 and E(Y) = 1, than what is E(XY)? 2) If X and Y are…

A: Solution is given below

Q: Suppose X and Y are jointly continuous random variables, the conditional expectation of u(x), given…

A: The conditional expectation of u(x) given y is:

Q: If two random variables X and Y are independent, then the covariance is zero, Cy=0, but the conyerse…

A:

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)2)? %3D

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Q: 4. Let X be a discrete random variable with E (X) = 3 and Var(X) = 0.5, What are the mean and…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: for r, y > 0, f(x, y) = (1+x)2.(1+xy)² > 0, otherwise. Show that X and X Y are independent,…

A: *answer:

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

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

A: Given : (X³ , 2 Y²-3 Y+4)

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 X be a random variable with p.d.f. 3e-3x 0<x<0 f(x) =- find E(e*) O.W

A: As per our guidelines we are suppose to answer first question .

Q: Let X and Y be independent random variables with E[X]=3, E[X^2] =25 E[Y] = 10 , E[Y^2] = 164  (d)…

A: We have given that,  Let X and Y be independent random variables with E[X]=3, E[X^2] =25 and E[Y] =…

Q: Let X1 ~ x² (n, 8) and X2 ~ x² (m, 2) : mX1 find the expected value of X = nX2 Е (X).

A: We have given two chi square distribution and we have to find the mean of  resultant F distribution.

Q: What value of C minimized B(X – C), where X is a random variable?

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Q: The amount of detergent in a box of a particular detergent has a uniform distribution with c=24 and…

A: The uniform distribution (continuous) is one of the simplest probability distributions in…

Q: The cdf of a random variable Y is |1– exp(-0.4y), y 20 F,(y) otherwise Valuate P{2.5 <Y < 6.2}.

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Q: applies to two random variables X and Y. (a) Show that X and Y are statistically independent (b)…

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Q: For two random variables X and Y, the following information is given. V(X)= 3, V(Y)=2 and cov(X, Y)…

A: Given that for two random variable X and Y,  VX=3VY=2cov(X,Y)=-1   The following variance propertied…

Q: || f(x,y)dxdy = 1 if X and Y are discret random variable

A: The objective is to state whether the statement is true or false. ∫-∞∞∫-∞∞fx,ydxdy=1  if X and Y are…

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: what is E[XY]?

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Q: Given the distribution function x < 0 1 0<x < 2 F (x) = 2 < x < 5 1 r25 of the random variable X.…

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Q: (TRUE / FALSE) For two random variables, X and Y , E(XY ) = E(X)E(Y ) if X and Y are uncorrelated.

A: Solution: The covariance between the random variable X and Y can be defined as  Cov(X,Y)= E(XY)-…

Q: The joint PMF of two random variables X and Y is given by (k(2x + y), ((2x) Pxy (x, y) 0, Where k is…

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Q: For the random variable X with the pmf f (x) = (x² + 4) , P(X = -1| a < 0) x = -2, –1,0, 1,2. Find…

A: Given Information: f(x) = 130x2+4 x = -2, -1, 0 , 1 , 2

Q: In the linear model, R2 is: OA. a regular random variable. OB. an observable fixed number.

A: The regression analysis is a statistical procedure that allow us to find the linear association…

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: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

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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

A: Random Variable: A random variable is a real valued function that assign a real number to each…

Q: the variances for independent random variables X and Y is Var(X)=D0.15 and Var(Y)=5.62 then Var…

A: Given If the variances for independent random variables X and Y is Var(X)=0.15 and Var(Y)-5.62 then…

Q: Let X and Y be independent random variables with X ~ N(0; 1) and Y~ N(0; 2). The value of P(X > Y )…

A: X follows Normal distribution with mean 0 and variance 1  Y follows Normal distribution with mean 0…

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: Suppose X and Y are independent random variables such that E(X)= 0, E(Y) = -1, Var(X) = 1, and…

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Q: X is a random variable with the probability distribution f(X)= :X= 0,1,2. Then the mean of X is…

A: Given function is: f(X)=X2;X=0,1,2

Q: Given that X and Y are independent random variables and E(X) = 4, E(Y) = 7,  Var(X) = 3,  Var(Y) =…

A: Given : X and Y are independent r.v with E(X) = 4 E(Y) = 7 Var(X) = 3 Var(Y) = 6

Q: Assume that X and Y are random variables with the following parameters: - 4 and oy 3, 13, Hy 12, Ох…

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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…

Q: The mean of the random variable X is ux = 38 and the coefficient of variation is Vx=0.37. Let Z be…

A: Z = x - μσ

Q: For a random variable X with mgf MX(t)=1/(1−4t)^1/2 i) Find E[X] ii)Find E[X^2]

A: Given the mgf of a random variable X  MXt=11-4t12

Q: For two random variables X and Y, var(X + Y) = var(X)+ var(Y)+2 Cvy and var(X – Y) = var(X)+…

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