Anya has three identical tea cups. She randomly stores each cup in one of three cupboards, where each cupb may contain more than one cup, and the choices are uniform and independent. Denote by X the number of cups in the rightmost cupboard, and denote by Y the number of non-empty cupboards. 1. Write down the joint distribution of (X,Y).
Anya has three identical tea cups. She randomly stores each cup in one of three cupboards, where each cupb may contain more than one cup, and the choices are uniform and independent. Denote by X the number of cups in the rightmost cupboard, and denote by Y the number of non-empty cupboards. 1. Write down the joint distribution of (X,Y).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Anya has three identical tea cups. She randomly stores each cup in one of three cupboards, where each cupboard
may contain more than one cup, and the choices are uniform and independent. Denote by X the number of tea
cups in the rightmost cupboard, and denote by Y the number of non-empty cupboards.
1. Write down the joint distribution of (X, Y).
2. Compute the marginal expectations E [X] and E [Y].
3. Compute the covariance Cov (X, Y) and the correlation coefficient px.Y .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3932aa1c-1b5f-4d84-a3d3-4f7705949611%2F9b29d7b2-2e24-4bb6-9b40-44030b988b51%2Fgllbez7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
Anya has three identical tea cups. She randomly stores each cup in one of three cupboards, where each cupboard
may contain more than one cup, and the choices are uniform and independent. Denote by X the number of tea
cups in the rightmost cupboard, and denote by Y the number of non-empty cupboards.
1. Write down the joint distribution of (X, Y).
2. Compute the marginal expectations E [X] and E [Y].
3. Compute the covariance Cov (X, Y) and the correlation coefficient px.Y .
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