The joint probability mass function of X and Y is given byP(1, 1) = 0p(2, 1) = 0.05p(3, 1) = 0.1(a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) =P(Y = :2|X = 2) =P(Y = 3|X = 2) =(b) Are X and Y independent? (enter YES or NO)(c) Compute the following probabilities:P(X+Y> 2) =P(XY = 3) =P(> 1) =p(1,2)= 0.1p(2, 2) = 0.3p(3,2)= 0.05p(1,3)= 0.05p(2, 3) = 0.1p(3, 3) = 0.25

We have given the joint probability distribution as…

Answered: The joint probability mass function of…

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

The joint probability mass function of Xand Ylis given by p(1, 1) = 0.2 p(2, 1) = 0.1 p(3, 1) = 0.05 p(3, 2) = 0.1 Р(1,2) - 0.1 p(2, 2) = 0.05 p(2,3) 0.05 p(1, 3) = 0.1 p(3, 3) = 0.25 %3D (a) Compute the conditional mass function of Ylgiven X 2: P(Y = 1|X = 2) D %3D P(Y = 2|X 2)= P(Y 3|X = 2) (b) Are Xland Yindependent? (enter YES or NO) NO
Let f, g be probability densities such supp(f) c supp(g). show yes X1, ... , Xn X1,..., X, iid. L(g) then f(X;) W; = g(X;) is hopeful 1. Argue why the weights need to be re-normalized even when the normalization constants of the densities f and g are known.
b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following probability density function: f(x;0)=√√2n0 0, -20₁ if -∞0 < x <∞0 otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 0.
The data for the joint probability mass function of X and Y (two different measurement systems) aregiven in the table below.a) Calculate the marginal distributions of X and Y and plot them.b) Select one of the Y values from the table and find the conditional probability mass function of X for thatY value you have selected and plot it.c) Show whether X and Y are independent or not.d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).
Suppose that p(x, y), the joint probability mass function of X and Y, is given by p(1, 1) = 0.5, p(1,2)= 0.1, p(2, 1) = 0.1, p(2, 2) = 0.3 Calculate the conditional probability mass function of X given that Y = 1.
The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(2, 1) = 0.1 p(1,2) = 0.05 p(1, 3) = 0.05 p(2,2) = 0 p(2, 3) = 0.05 p(3, 1) = 0.05 p(3,2) = 0.1 p(3, 3) = 0.55 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = ☐ P(Y = 2X = 2) = P(Y = 3|X = 2) (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X + Y > 2) = P(XY = 2) = P(¥ > 1) = |
b) Let Y1, Y2.,Y5 be independent random variables with probability density function y 1 e 4 4 f(y)= ,y > 0 ,elsewhere 3 Determine the distribution and parameter of V = EY; using the method of moment i=1 generating function. Hence, find the mean of V using the moment generating function.
Let X be a point randomly selected from the unit interval [0, 1]. Consider the random variable Y = (1-X)-¹/2 (a) Sketch Y as a function of X. (b) Find and plot the cdf of Y. (c) Derive the pdf of Y. (d) Compute the following probabilities: P(Y > 1), P(3 < Y < 6), P(Y ≤ 10).
Use a Venn diagram. Let P(Z) = 0.44, P(Y) = 0.28, and P(Z U Y) = 0.57. Find each probability. (a) P (Z'n Y') (b) P(Z'U Y) (c) P (Z' U Y) (d) P (Zn Y')
Let Y₁, Y₂,..., Yn be a random sample from the inverse Gaussian distribution with probability density function: f(y, μ, 2) = { Where μ and are unknown. a) What are i. 1 -ACT √ λ 2ny3)že elsewhere if y > 0 the likelihood ii. the log likelihood functions of u and λ. b) Find the maximum likelihood estimators of u and 2.
12. Let the random variable X and Y have joint pdf 4 f(x,y) = (x² + 3y²), 0

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