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# hmwk7 - ISyE 2027 R D Foley Probability with Applications...

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ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 7 October 25, 2006 due on Tuesday Please explain your answer to “yes” or “no” questions such as “are X and Y independent”. 1. (30 points) Leave your answer to in terms of ( n k ) . Suppose we are dealt 5 cards from a well-shuffled standard poker deck. Let X be the number of clubs and Y the number of diamonds in the hand. (a) What is the joint probability mass function of X and Y ? (b) What is the marginal probability mass function of Y (c) What is the conditional probability that X = 0 given Y = 4? 2. Roll a pair of dice where each die has 4 sides labelled with the numbers 1, . . . , 4. Let X be the maximum number rolled, and Y be the minimum of the rolled numbers. (a) What is the joint p.m.f. of X and Y ? (b) What is the marginal p.m.f. of X ? (c) What is the conditional p.m.f. of Y given X = 2? (d) What is the E[ Y | X = 2]? 3. Suppose ( X, Y ) has joint p.m.f. Pr { X = i, Y = j } = c (1 + i + j ) for i = 0 , 1 , 2 , j = 0 , 1 , 2 , i + j < 4.
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• Spring '08
• Zahrn
• Probability theory, Probability mass function, marginal probability mass, Poisson random variables, marginal p.m.f., R. D. Foley

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The text passage is a homework assignment for a probability course, containing multiple questions that require the calculation of probability mass functions, conditional probabilities, and expected values.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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# hmwk7 - ISyE 2027 R D Foley Probability with Applications...

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ISyE 2027 Probability with Applications Fall 2006 R. D. Foley Homework 7 October 25, 2006 due on Tuesday Please explain your answer to “yes” or “no” questions such as “are X and Y independent”. 1. (30 points) Leave your answer to in terms of ( n k ) . Suppose we are dealt 5 cards from a well-shuffled standard poker deck. Let X be the number of clubs and Y the number of diamonds in the hand. (a) What is the joint probability mass function of X and Y ? (b) What is the marginal probability mass function of Y (c) What is the conditional probability that X = 0 given Y = 4? 2. Roll a pair of dice where each die has 4 sides labelled with the numbers 1, . . . , 4. Let X be the maximum number rolled, and Y be the minimum of the rolled numbers. (a) What is the joint p.m.f. of X and Y ? (b) What is the marginal p.m.f. of X ? (c) What is the conditional p.m.f. of Y given X = 2? (d) What is the E[ Y | X = 2]? 3. Suppose ( X, Y ) has joint p.m.f. Pr { X = i, Y = j } = c (1 + i + j ) for i = 0 , 1 , 2 , j = 0 , 1 , 2 , i + j < 4.
This is the end of the preview. Sign up to access the rest of the document.
• Spring '08
• Zahrn
• Probability theory, Probability mass function, marginal probability mass, Poisson random variables, marginal p.m.f., R. D. Foley

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern
user
The text passage is a homework assignment for a probability course, containing multiple questions that require the calculation of probability mass functions, conditional probabilities, and expected values.

TYPE: MULTIPLE_QUESTIONS