Problem 6: Random variables X and Y have the joint CDF 0.5 (y + 1) (1 – e-2r), w 2 0 and |y| < 1, Fx,y(x, 9) 1 - - e-2r. x 20 and y > 1, 0, otherwise. (a) What is P(X s 1, Y < 0]? (b) What is P(X s 0, Y < 1]? (c) What is P(0 < X < 1,0 < Y < 1)?

Q: Find (a) The constant K (b) P(X> 1) (c) P(|x|<3)

A: To determine the value of K we will use the fact that the integration of pdf f(x) over whole range…

Q: 3. If a random variable X has a chi square distribution with v degrees of freedom, then E(X)= vand…

A: E(X)=v, V(X)=2V

Q: following (a) E(X) and E(Y) (b) Cov(X, Y) (c) Are X and Y independent? Justify your answer.

A: Solution

Q: cdf Co

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Q: (7) Suppose that X₁ and X₂ are two random variables with j.m.g. f. 2 (t₁ - 1)(t₂-1) + (t₂ − 1)² '…

A: It is given that the two random variables X1 and X2 has the m.g.f as below: MX1,…

Q: (c) w = 5ln(7r + 8) %3D O u = r' + 8, w = 5lnu O u = 7r, w = 5 (Inu + In8) O u = In(7r), w = 5 ln(u…

A: w=5 ln(7r+8)

Q: iv) E[E[Y²|X]]_ (EY)²

A: Note: As per you request, we have helped you solve only Part (iv) of the question.

Q: 4 Suppose ô² = 200 and b = [3 5 2] where D(b,) = 28 D(b2) = 24 v(b3) = 18 %3D côv(b,,b2) = -16…

A: Consider the linear model y,Xb,σ2where b'=b1  b2  b3. Let σ^2=200 and b^'=3  5  2 where…

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: Problem 4 Let X and Y be independent random variables. 1. Are X and -Y independent? (Hint: Use…

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Q: You place a token at the origin (0,0) of the square grid. You move token from one vertex to the…

A: Given:  The expression Initial position of the token = (0,0) The expression Final position of the…

Q: Example 3.12. Let X, Y and Z be jointly continuous random variables with joint PDF is given by:…

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Q: Find the means, variances and covariance of Y, and Y

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Q: Problem 2 Consider a random variable with cdf(x) = 1-exp(-10x) when x2 0. And 0 otherwise. a)…

A: Given that  Cumulative distribution function of X is  F(X=x)=1-e-10x  , x ≥ 0          = 0    ,…

Q: The random variable Y with density 1 fy)={v+n² y>0, |0, y<0. Develop a pseudo-code algorithm for…

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Q: 66. Consider two random variables X and Y with V(X) = 5, V(Y) = 10 and Cov(X,Y) = 3. (a) Find V(3X -…

A: V(X)=5 , V(Y)=10 and Cov(X,Y)=3

Q: 6. Suppose X1, X2, . X, is a random sample from the population that is uniformly distributed over…

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Q: Example 5: Let X1, X2 , X3 and X4 be independent random variables such that E (X;) = µ and Var (X;)…

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Q: Example R ² let X₁. X ₂0 Xn be a random sample from a distribution having f(x,0). +(x₂0) = { 0²…

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Q: Question 1. a) Consider an experiment which measures the value of three different vari- ables on a…

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Q: 3. Let (X,Y) be a bivariate random variable, and let a and b be real constants. Show that (a)…

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Q: 5. Let X and Y be random variables such that var(X)=16, var(Y) = 9, and p = cor(X,Y) = -0.5. %3D a.…

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Q: Example 3.6. Let X and Y be jointly continuous random variables with joint PDF is given by: Note…

A: We know from conditional probability ,   f X/Y (x/y) = f X,Y (x,y) / fY (y) and   f Y/X ( y/x) = f…

Q: 7. The integral domain (Z, +,.) can be embedded in the field (a) (Q, +,.) (b) (R, +,.) (c) (C,+,.)…

A: We know that every integral domain can be embedded in a field

Q: Let X and Y be independent random variables. 1. Are X and -Y independent? (Hint: Use Theorem: Let…

A:

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: (7) Suppose that X₁ and X₂ are two random variables with j. m. g. f. 2 (t₂-1)(t₂-1) + (t₂-1)²' - ²₁…

A: In the question, Given that X1 and X2 are two random variables having joint mgf given. Then We will…

Q: a) In regression analysis, to obtain the least square estimators of a and B, the SSR of Squares of…

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Q: Example 3.6. Let X and Y be jointly continuous random variables with joint PDF is given by: 3…

A: The handwritten solution

Q: C8) Prove that two continuous random variables, X, Y, with the bivariate cdf, F(s, t), are…

A: If a joint probability distribution of two random variables X and Y is fXY(x,y), then their marginal…

Q: Suppose we have three independent random variables X, Y and Z where... Var(X + 2Y) = 13, Var(2Y +…

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Q: 2. Two dimensional random variable (X, Y) is given by Y / X 1 2 -2 0 0,25 0,5 0,25 Find the…

A: GIVEN:         X         0 1 2 total   -2 0 0 0.25 0.25 Y 0 0 0.5 0 0.5   2 0.25 0 0…

Q: 2. The joint PDF of two random variables X and Y is given by far (x, y) = ÷(x² +).0 Y] c) Find Pr[Y…

A: It is an important part of statistics. It is widely used.

Q: 1.1 Consider Y₁, Y2,...,Yn are i.i.d. random variables with n > 4 and T is the sample mean Y. Also…

A: From the given information, Y1, Y2,…………..,Yn are i.i.d random variables.

Q: 1) Determine the value of c. 2) Find (a) P{|x| < 1}, (b) P{X² < 9}, and (c) P{X = 1}

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Q: If the moment-generating function of a random variable X is Mx(t)=(1-5t (a) Find E(X). (b) Find a…

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Q: 4. Suppose X₁ and X₂ are independent random variables with cdf Fx (x) = sin(x), 0 ≤ x ≤ 1/ a. Show…

A: and  denote  random variables.The CDF:

Q: 25. The random variables X and Y have the joint probability function f(x, y) = K(4- x- y); 0<x<2; 0<…

A: