X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X + b Y), where a and b are arbitrary constants.  The final answer is an expression.

Q: If the random variable X follows N (0, 2) and Y = 3X, find the mean and vari- %3D ance of Y.

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Q: Let X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random…

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A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

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A: Given that Y = 75 - 3X - X2,  E(X2) = 12, and E(Y) = 54

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A: Let  y be a contineous random variable wherefy=118,-3≤y≤150,     otherwise

Q: Suppose that X and Y are random variables. If we know that V(X)=11 and Y=2X−4, determine σ(Y).

A: Given : V(X)=11 and Y=2X−4 V(Y) = V(2X−4) = 22V(X) = 4*11 = 44

Q: Suppose for a random variable X that E(X) = 5 and Var(X) = 3. What is E((X + 3)²)? Type your answer.…

A: By the properties of random variable, Expectation of constant is a constant. i.e., E(a)=a Variance…

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Q: X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X +…

A: Given that ; Var(x) = 4 Var (y) = 6 Var(x+ y) = 16 By using variance property we solve it

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Q: Let X and Y are two random variables. Find Var(2X – 3Y ) Select one: a. Var(2X - 3Y) = 4Var(X) –…

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

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

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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: vo random variables X-(-1,0) and Y=(2,3) are equiprobable and independent. Determine the

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Q: Let X and Y be random variables such that var(X) = 16, var (Y) = 9, and p = cor(X, Y) = -0.5. a.…

A: Solution

Q: Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate…

A: Given Data: Var(X)=8 Var(Y)=6

Q: Show that for two random variables X and Y, 2 2 var(aX+bY) = a¹o²+b²oy² + 2ab Cxx XY where a and b…

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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 X and Y be two random variables such that Cov(X.Y)=-3. Then cov(3X+5,-2Y+5)=18…

A: It is given that The covariance between X and Y is Cov(X, Y) = -3 We know that Cov(aX+b, cY+d) =…

Q: Show that the random variables X and Y are not independent and find P(X = 0|Y_ 2), P(X = 1|Y = 2),…

A: For the independence of two variables, we must have P(X = x, Y = y) = P(X = x).P(Y=y)

Q: If X1 and X2 are independent random variables with distribution given by P[Xi] = −1 = P[Xi = 1] =…

A: Construct the PMF of X1X2, So, P(X1X2 = x) = P(X1=1, X2 = 1) +P(X1=-1, X2 = -1)    if x =1P(X1=-1,…

Q: Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X,…

A: Given that the mean of aX+bY is 3  So,  E(aX+bY)=3aE(X)+bE(Y)=3a(1)+b(2)=3a+2b=3a=3-2b ..........(Eq…

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: PMF of random variable X is defined as 0.2 X = -2 0.1 X = -1 0.1 X = 0 Px (x) = {0 X = 1 ve X = 2…

A:

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

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Q: III. Prove that the mean and variance of a binomially distributed random variable are, respectively,…

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Q: Suppose that X and Y are both binomial random variables with parameters n and p. If Var(X − Y) = 2,…

A: SOLUTION: Cov(X,Y)=np(1-p)-1

Q: The cdf of a continuous random variable X is given. Find P(2.4<X<6.1). if x s2 F(x) = 0.2x -0.4 if…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose that X and Y are random variables with E(XY) = E(X)E(Y). Then X and Y * independent. Also…

A: E(XY) = E(X)E(Y)

Q: IfXand Y are Two Random Variables and X, Y and o,, are the Corresponding Means and Variance of X and…

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Q: For a discrete random variable X, find Var(X) if* Var (5 - 2X) = 12 a)2 b)1 c)3 d)6

A: It is given that, Var (5 - 2X) = 12

Q: If two random variables X and Y are independent, then Mxy (V1,V2) = Mx (V, ) M, (v2) %3D XY

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Q: If X(n,p) is a binomial random variable with parameters n and p, then why is it that X(n+1,p)…

A: Given that X(n, p) is a binomial random variable with parameters n and p.We will prove the given…

Q: (6) Let X and Y be random variables with var(X) = 4, var(Y) = 9 and %3D var(X – Y) = 16. Then…

A: Given: Var(X) = 4 Var(Y) = 9 Var(X-Y) = 16

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Q: (a) What is the probability that X + Y > 1.

A: Exponential distribution is widely used in statistics . It has the unique lack of memory property .

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