Suppose that p(x, y), the joint probability mass function of Xand Y, is given byp(1, 1) = 0.5, p(1,2)= 0.1, p(2, 1) = 0.1, p(2, 2) = 0.3Calculate the conditional probability mass function of X given that Y = 1.

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Answered: Suppose that p(x, y), the joint…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The joint probability mass function of X and Y is given by P(1, 1) = 0 p(2, 1) = 0.05 p(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)= 0.1 p(2, 2) = 0.3 p(3,2)= 0.05 p(1,3)= 0.05 p(2, 3) = 0.1 p(3, 3) = 0.25
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).
Explain A, B, C
The joint probability mass function of X and Y, p(x,y) is given by p(1,1)= p(2,1)= p(3,1)= p(1,2)=p(2,2)=0 p(3,2)= 18 p(1,3)=0 p(2,3)= p(3,3)=1² a) b) c) Calculate E(X) and Var(X). Compute E(X | Y = 1) and Var(X|Y=1). Are the random variables X and Y independent?
Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. FInd (d) fZ|XY (z|x,y), (e) fX|YZ(x|y, z).
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.
c) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
Suppose that the random variables Y1 and Y2 have joint probability density function, f(y1, y2), given 6y y2, 0syı < y2, y1 + y2 < 2 fV1, y2) = - 0, elsewhere Derive the marginal density of Y1. Derive the marginal density of Y2.(Hint: this will have to broken down into two parts!!!) Derive the conditional density of Y2 given Y1 = y1. Find P(Y2 < 1.1 | Y1 = .60). %D
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.

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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.