Q3| The jpmf of the random variables X and Y is given by (x, y) = (1,2), (3,2) 12 1 pxy(x, y) = {6 (x, y) = (2,2), (3,3), (1,3) 1 (x,y) = (2,4) 0.W Find: a) P(x=2/y33) b) P(x/y=4)

Q: The discrete random variable X has the probability distribution 2 4 P(X=x) k 2k 3k 4k 3.

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Q: ii) Let X be a random variable taking three values: P(X= a₁) = P₁, P(X=a₂) = P2, P(X=a3) = P3, where…

A: Given Information: Let X be a random variable taking three values: PX=a1=p1, PX=a2=p2, PX=a3=p3,…

Q: A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1…

A: Given: Let X be a Poisson random variable. The probability mass function is provided as:…

Q: For events A and B we have P(A) = 0.3, P(B) = a and P(AUB) = 0.7. Then the value of a if A and 4. B…

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

Q: Which of the following is equal to Cov (X+ Y, 2X +Y), where X and Y S ? are random variables on a…

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Q: A discrete random variable Y is such that 1 y(y + 1)' P(Y = y) = y = 1, 2, 3, ...

A: Given:Y is a discrete random variable.P(Y=y)=1y(y+1),       1,2,3,.....Find:E(Y)

Q: Suppose that x and y are two random variables such that H(X)=7/4 bits, H(Y)=2 bits, H(X|Y)=11/8…

A: Given : H(x) = 7/4 H(y) = 2 H(x|y) = 11/8 H(x,y) = 27/8 We have to calculate I(x, y)

Q: For any two random variables Y₁ and Y₂, Var(Y₁Y₂|Y₁ = y₁) = y{Var(Y₂|Y₁ = y₁). TRUE

A: Given that Y1 and Y2 are two random variables. Formula: If X is a random variable, then VX=EX2-EX2.…

Q: Suppose that X andY are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y?) = 30 and…

A: Given that ; E(x) = 2   ;    E(x2 ) = 8  ; E(y) = 5  ;    E(y2 ) = 30 By using these information we…

Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

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Q: Let X and Y be two independent N(0,1) random variables and consider Z = 3 + X+ 2XY² , W = 5+ X. Then…

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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: (a) (b) Find E(W). Find Var(W).

A: Given,let  be  independent random variables.E(Yi)=μ and Var(Yi)=σ2  for every since (a)we want to…

Q: We have the following information about the random variables X and Y: |x=2, |y=−1 , ox = 0.25, c X…

A: a)It is given that, .

Q: Two random variables X and Y are defined by X = 0, Y =-1, X² = 2, y² = 4 and Ry -2. Two new random…

A: Given : X¯=0Y¯=-1X2¯=2Y2¯=4RXY=-2W=2X+YU=X-3Y

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 the sample space S= {(-2, 4), (-1, 1), (0, 0), (1, 1), (2,4)}, where each point is assumed…

A: I find the the value of cov(X,Y) using r-software.   R-code:- x = c(-2,-1,0,1,2) y = c(4,1,0,1,4)…

Q: (a) The correlation

A: Answer:

Q: Show that if X and Y are independent Exp(a)-distributed random vari- ables, then X/Y e F(2, 2).

A: The distribution of a continuous random variable can be identified by its pdf because the pdf of…

Q: Let X, Y and Z be three independent random variables such that E(X)=E(Y)=2E(Z)=2 and…

A: Variance of a Random Variable: The variance of a random variable X is defined as a measure of…

Q: Suppose that X and Y are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y²) = 30 and…

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Q: Let X_1 and X_2 be independent random variables for which P(X_i = 1) = 2/5 and P(X_i = 2) = 3/5.…

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Q: Let X be a random variable such that E(X) = 5 and V(X) = 4. The mean and the variance of 3X+4 are…

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Q: 2. Let X be a random variable with p.m.f., (1+x? 20X = -1,0,1,2,3 0 ,otherwise. f(x) = Find E(3X² +…

A: Given function isf(x)={1+x220,    x=-1,0,1,2,30         ,   otherwise

Q: Show that if X, Y are independent random variables, then Cov(X, Y ) = 0.

A: Given that X and Y are independent random variables.

Q: 5. Show that given random variables X and Y, Cov(X, E(Y | X)) = Cov(X, Y).

A: For the random variable X and Y, we need to show that: Cov[X, E(Y|X)] = Cov(X,Y)

Q: Let X_1 and X_2 be independent random variables for which P(X_i = 1) = 2/5 and P(X_i = 2) = 3/5.…

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Q: Let X ∼ N (0, 1) and Y ∼ Ber(p) be two independent random variables. find the law of S = X + Y

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Q: Let X_1 and X_2 be independent random variables for which P(X_i = 1) = 2/5 and P(X_i = 2) = 3/5.…

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Q: 4 of these 5 of these 3 of (a) 1.0211 (c) 1.5207 (e) 1.2962 these 2 (a) 0.1111 (c) 2.3333 (e)…

A: Introduction: There are a total of 16 tickets in the box. The random variable X denotes the number…

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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