**Title: Understanding Probability Distribution Transformation****Objective:**Learn how to determine the probability distribution of a transformed random variable.**Problem Statement:**Let the random variable \( X \) have the probability distribution listed in the table below. Determine the probability distribution of the random variable \((X + 1)^2\).**Given Probability Distribution:**| \( k \) | \( \Pr(X = k) \) ||---------|-----------------|| 2 | 0.2 || 3 | 0.2 || 4 | 0.2 || 5 | 0.3 || 6 | 0.1 |**Task:**Fill in the table for the probability distribution of the variable \((X + 1)^2\).**Transformations:**- When \( X = 2 \), \((X + 1)^2 = 3^2 = 9\).- When \( X = 3 \), \((X + 1)^2 = 4^2 = 16\).- When \( X = 4 \), \((X + 1)^2 = 5^2 = 25\).- When \( X = 5 \), \((X + 1)^2 = 6^2 = 36\).- When \( X = 6 \), \((X + 1)^2 = 7^2 = 49\).**Table for \((X + 1)^2\):**| \( k \) | \( \Pr((X + 1)^2 = k) \) ||---------|-------------------------|| 9 | || 16 | || 25 | || 36 | || 49 | |**Instructions:**Calculate the probabilities for each transformed value and fill the table. The probability for each value is the sum of probabilities that map to it based on the transformation.**Example Calculation for Clarity:**Determine \(\Pr((X + 1)^2 = 9)\):- Based on transformation, \(\Pr(X = 2)\) fully contributes to \(\Pr((X + 1)^2 = 9)\).- Therefore, \(\Pr((X + 1)^2 = 9) =

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Answered: Let the random variable X have the…

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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