Let X and Y be two random variables such that Cov(X.Y)=-3. Then cov(3X+5,-2Y+5)=18 cov(5X+3.-2Y-2)--20 cov(-3X+5-3Y+5)=-18 None of these

Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?

A: Solution

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

A: At first remind that                                      Independent ⇒UncorrelatedBut, Uncorrelated…

Q: If X and Y are random variables such that E[2X + Y] = 0 and E[X + 2Y] = 33, then %3D E[X] + E[Y] %3D

A: Given  E(2X+Y)= 0 E(X+2Y)=33 We need to find E(X)+ E(Y)

Q: Let X and Y be two random variables such that: Y = 75 – 3X – X2, E(X²) = 12 and E(Y) = 54. Then V(X)…

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

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

A: We know that if X and Y are independent then E(XY)=E(X)E(Y). But the converse is not always true.…

Q: If X and Y are two random variables, then the covariance of x+a,Y +b,where a and b are constant is…

A:

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: (A) ơy = 0xı + Ox2 Vox1 + Ox2 +o? = Ox1 +0x2 (B ) συ .2 (C) oy = -2 x2 X1 .2 -2 (D) Oy/y = X2

A: The standard deviation is not directly added together but the variance is added for variables. So…

Q: Let X - Po(A), A > 0. Determine the PMF of the random variable Y = X² – 3 and

A: Poisson distribution: A random variable X is said to have a Poisson distribution with a parameter λ…

Q: Two random variables share the same range of numerical values (0,1,2,3} and their joint PMF is given…

A: Let , X and Y denote random variables of the discrete type , with joint pmf PXY(x,y) which is…

Q: Let Y1 and Y2 be independent random variables that are both uniformly distributed on the interval…

A: Consider that Y1 and Y2 are two continuous real valued random variables with joint probability…

Q: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Var(aX) = 16 Var(bY) = 36…

A: Suppose we have two random variables X and Y. For a, b > 0, a2+b2=13. Here we use the…

Q: Q24. Gaussian random variables X, andX, for which, = 2, o%, = 9, X2 =-1, ox, = 4 and CX =-3, are…

A: If two variables are Gaussian then their linear combination will also follow the Gaussian…

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: We want to find V(aX+bY)= ?

Q: a) Let X, Y and Z be random variables. Show Cov(X + Y,Z) = Cov(X,Z) * Cov(Y,Z). %3D

A: Note: Hey there! Thank you for the question. Each of the questions (a), (b), (c), (d), and (e) is a…

Q: It is known that X is a random variable with PMF Px(x) = cx? for x = Px(x) = 0 otherwise. Each…

A: Solution

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: Suppose that X and Y are independent normal random variables and - XE N(6,1) Y € N(8, 2) Find P(X -…

A: We have given that , X€N(6,1)       Y€(8,2) . We have to find, P(X-Y>0) = ?

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 joint CDF of the random variables X and Y is given by: 0, x < -2 or y < -5 3/8,…

A: From the given information, The joint CDF of X and Y is, FX,Y=0, x&lt;-2 or y&lt;-538, -2≤x&lt;2,…

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: For two random variables X and Y. If o xy= 0, then X and Y may not be independent. Select one: True…

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

Q: Let X1 and X, be any two random variables, then V( X1 + X2 ) must be: OA. greater than: V(X1 ) +…

A: Following are the two concepts that are used to explain the two variables. These are expected value…

Q: X and Y are random variables that are both Normally Distributed. The Mean of X is 5 and its SD is 3.…

A: Given that  P(4 &lt; Y &lt; 16) = P(A &lt; X &lt; B) μX=5σX=3μY=-2σY=6

Q: Let X be a random variable taking only the values 0, 1, 2, 3, 4 with probabilities given by P(X = 0)…

A: Discrete probabilty  The conditions of the probability is 1) p(x) ≥ 0 2) Σp(x)=1

Q: Suppose you have joint random variables X and Y. a) If a problem does not state anything about…

A: X and Y are 2 R.V. and if the dist. of X is not influenced by Y values then 2 R.V. are independent.

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: Let X and Y be two random variables such that cov(x.y) 10 var(x)=16 var(y)=64 then var(x-2y+7)= 168…

A: Let X and Y be two Random Variables  s.t  covx,y=10, varx=16, vary=64   then varx-2y+7=?

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: 3- Show that, if the random variables X and Y are N(0 6,0",r) , thên 1 a) E{ fy(y|x)} = =exp{- 20…

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Q: We have two independent random variables X, and X2. Let X,~N(5,15) and X2~x?. Calculate P(X, – 5 >…

A:

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 random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

Q: Let V=X+Y and U=X-Y are random variables, then the condition which make the covariance

A: Given that V=X+Y and U=X-Y are random variables. Formula for covariance between U and V is…

Q: X, =2, o =9, X2 =-1, ox, = 4 and Cx,x2 =-3, are transformed to new random variables Y, and Y,…

A:

Q: Let x1  and x1 be independent standard normal random variables. If Y1= x1 + 2x2 and  Y2 = 2x1 - x2,…

A: We know, any linear combination of normal distribution is a normal distribution. Here, x1 and x2 are…

Q: Consider random variable X whose CDF is given as follows -1 (a) Let Y = X2. Then find CDF and PDF of…

A: ...

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…

A:

Q: Let Y1 and Y2 be independent random variables with Y; ~ N (0, 1). 1 Let 1-[":]+c[ %] where C:2 x 2 =…

A: From the given information, Y1 and Y2 are independent random variables with Yi~N0, 1. That is,…

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: Let X and Y be any two random variables and let a and b be any two real numbers. Then var(ax + bY) =…

A: We know that ; For any constants  and b ;  Var(aX + bY) = a2V(X) + b2V(Y)+2 ab Cov(X,Y)

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…

A:

Q: Suppose X and Y are independent random variables with X - B (n, p) and Y ~ B (m, p). Show that X +Y…

A:

Q: Suppose that X1,., Xn are iid random variables with 2 P(X; = 0) P(X; = 1) : 3 P(X; = 2) (1 – 0) %3D…

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

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

Q: If X is uniform random variable on interval (2,7) then the expexted value of X equal 9/2 (1/2 (5/2

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Let X and Y be two random variables such that Cov(X.Y) = -3 . Then %3D O None of these O…

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Q: Let X be a random variable with p.d.f f(x) =x(9-x), 0sxS 3. Find the mode.

A: Introduction Mode: Mode is one of the types of measures of central tendency. Mode is the location…