7. Suppose X and Y are discrete random variables with the following joint pmf.I123Py(y)1T40P1010y2T1021010610(a) Are X and Y independent? Prove your claim.Px(x)21010101(b) Find E(X). Express your answer as a fraction in lowest terms.(c) Find Var(Y). Express your answer as a fraction in lowest terms.(d) Find E(3Y2 - 2X+5). Express your answer as a fraction in lowest terms.

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Answered: 7. Suppose X and Y are discrete random…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X be a random variable defined by 2 3 P(X = x) k 2k 2k 2k 2k Then E(X) and V(X) are equal to: None of these O E(X)=13/5 and V(X)=41/25 O E(X)=20/9 and V(X)=140/81 O E(X)=27/11 and V(X)=206/121
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y)=-7 Var (X) = 20 Var (Y)=6 Var (z) = 23 E (X) = 5 E(Z) = 3 Compute the values of the expressions below. E (-2X – 4) = -3Z + 2X E 3 Var (27 + 3) - O =(-sx") - O
.Two random variables X and Y have the joint pdf, fx y(x, y) = Ae-2x+y), x, y 2 0 elsewhere
6. and let Consider a random variable X with the following distribution a P(X= x) 1 0.2 Y = 3 4 7 0.25 0.1 0.35 1, 2, 3, X <3 X 27 otherwise. (a) What are the mean and variance of X? (b) What are the mean and variance of Y? (c) Are X and Y independent? Justify with a formula. (d) Find Cov(X, Y) and the correlation coefficient pxy. 8 0.1
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-1 E(Y) = 4 E (Z)=0 Var(X)=20 Var(Y) = 27 Var (Z) = 38 Compute the values of the expressions below. E (5Z-2) = 0 2Z+X -5 Var(2X-3) = 0 E = E (32²) = 0 Explanation Check X O hp Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Term
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Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27
(3) Let X be a random variable with p.d.f 2 (3x+6) 15 then E(x) is 11 12 (b) 30 (c) 30 (d) (e) None of these 33 716
I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?
4. A particle moves on the x- axis starting at x = 0. With equal probability, the particle moves to the left or right one unit. Let X denote the position on the x- axis after four moves. (a) Find px(x). Notice that X can take on -4,-2,0, 2, 4. Fill out the table below. xPx(x) (b) What is the expected position of the particle after four moves. That is, compute E(X). Express your answer as a fraction in lowest terms.
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(1) Let X be a random variable with a function k(3x2 +6) f(x) =- -1,0,1,2 then O.w 1 1 1 (a) k = 44 (b) k =- 43 7 (c) k = 42 (d) k (e) None of these 44 a is the correct answer b is the correct answer O c is the correct answer d is the correct answer e is the correct answer

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