The image contains a statistical exercise involving probability distributions for a random variable \( Y \). On the left, there's information about the probability distribution of \( Y \), and on the right, there's an incomplete table to be filled out for the transformed variable \(\frac{1}{5}Y\).### Left Side:#### Problem Description:"Let the random variable \( Y \) have the probability distribution listed in the table below. Determine the probability distributions of the random variable \(\frac{1}{5}Y\)."#### Probability Distribution of \( Y \):| \( k \) | \( \Pr(Y = k) \) ||---------|------------------|| 5 | 0.2 || 10 | 0.3 || 15 | 0.2 || 20 | 0.2 || 25 | 0.1 |### Right Side:#### Task:"Fill in the table for the probability distribution of the variable \(\frac{1}{5}Y\)."#### Incomplete Table:The table to be filled:| \( k \) | \( \Pr\left(\frac{1}{5}Y = k\right) \) ||---------|---------------------------------------|| 1 | [ ] || 2 | [ ] || 3 | [ ] || 4 | [ ] || 5 | [ ] |The task consists of using the given probability distribution of \( Y \) to calculate the corresponding probabilities for \(\frac{1}{5}Y\) and fill out the right-hand table.

Answered: Image /qna-images/answer/f78916a1-34a8-44a0-a035-3e7fd667607e.jpg

Answered: Let the random variable Y have the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let the random variable Y have the probability distribution listed in the table below. Determine the probability distributions of the random variable k 5 15056 20 25 Pr(Y=k) 0.2 0.3 0.2 0.2 0.1 Y. Fill in the table for the probability distribution of the variable Y. 5 k 1 2 3 4 5 Pr(=Y=k)