/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q3E Suppose that X and Y have a ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Suppose thatXandYhave a discrete joint distribution for which the joint p.f. is defined as follows:


Short Answer

Expert verified

a. The value of the constant is 0.025.

b. The probability is 0.05.

c. The probability is 0.175.

d. The probability is 0.70.

Step by step solution

01

Given the information

02

Finding the value of constant

The value of the constant is 0.025.

The joint pmf of X and Y is given by,


03

Calculating the probability for part (b)

b.

Pr (X=0 and Y = -2) = 0.025|0-2|

= 0.05

The probability is 0.05

04

Calculating the probability for part (c)

05

Calculating the probability for part (d)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that a random variableXhas the binomial distribution

with parametersn=8 andp=0.7. Find Pr(X≥5)by using the table given at the end of this book. Hint: Use the fact that Pr(X≥5)=Pr(Y≤3), whereYhas thebinomial distribution with parametersn=8 andp=0.3.

Suppose that each of two gamblersAandBhas an initial fortune of 50 dollars and that there is a probabilitypthat gamblerAwill win on any single play of a game against gamblerB. Also, suppose either that one gambler can win one dollar from the other on each play of the game or that they can double the stakes and one can win two dollars from the other on each play of the game. Under which of these two conditions doesAhave the greater

probability of winning the initial fortune ofBbefore losing her own for each of the following conditions: (a)\(p < \frac{1}{2}\);

(b)\(p > \frac{1}{2}\); (c)\(p = \frac{1}{2}\)?

Suppose that the joint distribution of X and Y is uniform over the region in the\({\bf{xy}}\)plane bounded by the four lines\({\bf{x = - 1,x = 1,y = x + 1}}\)and\({\bf{y = x - 1}}\). Determine (a)\({\bf{Pr}}\left( {{\bf{XY > 0}}} \right)\)and (b) the conditional p.d.f. of Y given that\({\bf{X = x}}\).

A civil engineer is studying a left-turn lane that is long enough to hold seven cars. LetXbe the number of cars in the lane at the end of a randomly chosen red light. The engineer believes that the probability thatX=xis proportional to(x+1)(8−x)forx=0, . . . ,7 (the possible values ofX).

a. Find the p.f. ofX.

b. Find the probability thatXwill be at least 5.

Question:Suppose that a point (X,Y) is to be chosen from the squareSin thexy-plane containing all points (x,y) such that 0≤x≤1 and 0≤y≤1. Suppose that the probability that the chosen point will be the corner(0,0)is 0.1, the probability that it will be the corner(1,0)is 0.2, and the probability that it will be the corner(0,1)is 0.4, and the probability that it will be the corner(1,1)is 0.1. Suppose also that if the chosen point is not one of the four corners of the square, then it will be an interior point of the square and will be chosen according to a constant p.d.f. over the interior of the square. Determine

\(\begin{array}{l}\left( {\bf{a}} \right)\;{\bf{Pr}}\left( {{\bf{X}} \le \frac{{\bf{1}}}{{\bf{4}}}} \right)\;{\bf{and}}\\\left( {\bf{b}} \right)\;{\bf{Pr}}\left( {{\bf{X + Y}} \le {\bf{1}}} \right)\end{array}\)

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.