Section I 3. Suppose that X is a discrete random variable with pmf |4- r|+ 4 f(z) for =-6,-3,0,3,6, C where c is a constant. (a) Find c.

Q: Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An…

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

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: Prove let B= 6+ I %3D : m = ',2,3, 3m S. Then inf(8) =6

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Q: (45) Let X be a random variable with p.d.f. ((k + 4)(x+2) 0<x<2 f(x)=- find (1) k (2) E(x) O.W

A: (45) (1) The random variable X with p.d.f is, fx=k+4x+2      0&lt;x&lt;20…

Q: Problem 2. Let X1,..., X, be any n random variables such that |Cov(X;, X;)| < 0, i, j 1,..., n. Let…

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Q: Section II 11. Assume X is a random variable with moment generating function M(t) (0.3e" +0.7), -00…

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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: 3- , thei a) E{f,(y\x)} =- exp(- o/27(2-r²) 20ʻ(2-r²)' 1 b) E{f, (x)f;(y)}=- 2.noV4-r

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Q: Show works! Let Xn be a random variable and mn be a median of Xn, n =1,2,.... Show that if Xn →d X…

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Q: We know that X is an unknown distribution with a mean of u and a variance Xị are i.i.d. e

A: From the given information, X is an unknown distribution with a mean of μ and a variance of σ2; And…

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

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Q: Recall: X(n, p) is a binomial random variable means P(X = x) = p*(1 – p)"-* x(n-x) Let X(n, p)…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: 3. If X and Y are independent uniform (0, 1) random variables, show that 2 for a > 0 (a + 1)(a + 2)…

A: X and Y are independent U(0,1) random variables:Objective: Show that:

Q: (3) Let X be a random variable with p.df 12(3x+ 0<x<1 15 , then P(0<x< 0.5) is o.w 7 (d) 7 (a) 60…

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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: . Let Y be a continuous random variable where f(y) F(y)? (a) Y 18 Y 15 Y-3 18 y+3 (b) (c) (d) 18 (e)…

A: The random variable Y is a continuous random variable with pdf f(y) = 1/18 ; -3 ≤ y ≤ 15

Q: Q2. Two events A and B are said to be dependent if and only if:

A: Here use basic of dependent events

Q: 2 - 4. X, X2, .. is a random sample of N (0,1), find the (X, +X,) Jox,-X2) distribution of Y

A: Solution

Q: (3) Let X be a random variable with p.d.f -(3x+6) 15 0<x<1 f(x) =- then E(Gx) is O.w 4 7 15 (b) 15…

A: We want to find correct answer for question

Q: (1) Let X be a random variable with a function x= 0,1, 2,3 4 xt(3-x)! S(x)=- , then E(x+1) is o.w…

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Q: 1-4x and 4 1+3x 1-x 1+2x (5) If a random variable assumes 4 values with probability the 4 4 4…

A: If the random variable assumes 4 values , then the sum of all probabilities for x should be equal to…

Q: (1) Let X be a random variable with a function (3 4 x! (3-x)! S(x) =- x= 0,1, 2,3 . then E(x+1)is…

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Q: Gaussian random variables X₁ and X₂ whose X₁ = 2,0x²=9₁ X₂ =−1, 2 = 4 and Cx₁x=-3 are transformed to…

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Q: (1) Let X be a random variable with a function [3 1 x= 0,1,2,3 4 x! (3-x)! fx) = { , then E(x) is…

A: Given, X is a random variable with the function below

Q: 17. Let X1, X2, and X3 be independent, U (0, 1)-distributed random variables. Compute P(X(3) > 1/2|…

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Q: (1) Let X be a random variable with a function (3 1 4 xt (3-x)! *- 0,1, 2,3 , then E(x+1) is o.w (e)…

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Q: Suppose that X is a random variable * ? having the following p.d.f. , Find Var(x) { 2(1 – x) 0 < x <…

A: Given: f(x)=2(1-x) , 0&lt;x&lt;1 The formula to compute the mean is: V(x)=∫x2fx dx-∫xfx dx2

Q: Example: (k (x+1) p(x) = P) is p.d.f. I x = 1,2,3,4 elsewhere Ep(x)=1 k(1+1)+ k(2+1)+k(3+1)+ k(4+1)…

A: Given, Probability mass function is: P (x) = k (x+1)                x = 1, 2, 3, 40…

Q: Let X be a discrete random variable with pmf (a) Find the pmf for Y = X². (b) Find the pmf for U = X…

A: The PMF of random variable X is: f(x)=18      x=-214      x=-114      x=014      x=118       x=2  0…

Q: You perform an experiment n times, each of which has a probability p of success. What's the…

A: From the provided information, We perform an experiment n times. The number of trials = n The…

Q: -. Determine the constant c so that f(x)=cx, x=1, 2, 3,...,10 satisfies the conditions of being a p.…

A: The given probability distribution can be desctibed as X 1 2 3 4 5 6 7 8 9 10 f(x) c 2c 3c 4c…

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

A: # given random variable x and y  Then cov(2x+y,x-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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