Q4 Consider two random variables X and Y. The probability mass function of X is {p(3)-1/4,p(4)=1/2, p(5)-1/4}, and the probability mass function of Y is {p(1)-1/12, p(2)-1/8, p(3)-1/6,p(4)=1/4, p(5)-1/6, p(6)-1/8, p(7)-1/12).Find the expectation and variance of X and Y? (With drawing)

Farmula used V(X)=E(X2)-[E(X)]2

Answered: Q4 Consider two random variables X and…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

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

See similar textbooks

Similar questions

A Gaussian random variable has a PDF of the form √ fx(x) = (a) Pr(X>0), (c) Pr(X 3), (g) Pr(X+2] > 1), NT exp(-2(x + 1)²). Write each of the following probabilities in terms of Q-functions (with positive arguments) and also give numerical evaluations: (b) Pr(X>2) (d) Pr(X<-4), (f) Pr(|X+1 <2) (h) Pr(X-1<2)
Prove the theorem
Let (X1, X2, X3) be the random outcome of tossing a fair six-faced die three times, and let (Y(1), Y(2), Y(3) be the order statistics from (X1, X2, X3). We have Y(1) = min (X1, X2, X3), Y(3) = max (X1, X2, X3), and Y(1) < Y(2) < Y(3). Find Pr (Y(1) = 3).
Let X be a random variable with pmf P(O)=0.2, P(1)-0.5, P(2)=0.3. Let F(X) be the cdf of X. (a) Find P(X<0.7) (b) Find F(1.3). (c) Find F(3).
another random variable Y. The joint probability masS function of X and Y is dter random variable Y. The joint probability mass function of X and Y is listed below. am put to a communication channelis a random variable X and the output is Y/X -1 1/4 1/8 -1 Р (Х, Y) %3D 1/4 1 1/8 1/4 Find (a) P (Y=1/X=1) (b) P (X=1/Y=1)
(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
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) = 4 Var(X) = 24 Var(Y) 18 Var(z)=7 E(X)= -3 E(Z) =-1 Compute the values of the expressions below. E(-4-5X)= 0 %3D ? ()- 0 Var(-3+2.X) = 0
c d
4 of these 1 5 of these 3 of (a) 1.0211 (c) 1.5207 (e) 1.2962 these 2 (a) 0.1111 (c) 2.3333 (e) 12.9375 2 of these 16 tickets total 3 FIG. 5. 2 of these 26. Let X be the random variables described in Fig- ure 5. Find E(√x + 1). (b) 2.3125 (d) 0.4613 X Random draw from the box 27. Let X be the random variable described in Figure 5. Find E(X³ | X < 2). (b) 0.5625 (d) 1.3125

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Q4 Consider two random variables X and Y. The probability mass function of X is {p(3)-1/4, p(4)=1/2, p(5)-1/4}, and the probability mass function of Y is {p(1)-1/12, p(2)-1/8, p(3)-1/6, p(4)=1/4, p(5)-1/6, p(6)-1/8, p(7)-1/12). Find the expectation and variance of X and Y? (With drawing)