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Anya has three identical tea cups. She randomly stores each cup in one of three cupboards, where each cupboard nay contain more than one cup, and the choices are uniform and independent. Denote by X the number of tea ups 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 cupboard nay contain more than one cup, and the choices are uniform and independent. Denote by X the number of tea ups in the rightmost cupboard, and denote by Y the number of non-empty cupboards. 1. Write down the joint distribution of (X, Y).

A First Course in Probability (10th Edition)
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...
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Solve 2nd part only plz solve it now in 20 min plz..
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 .
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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