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Let the random variable X have the probability distribution listed in the table below. Determine the probability distribution of the random variable X-3. k 1 2 3 4 5 Pr(X=k) 0.3 0.1 View an example 0.2 0.3 0.1 Get more help - MacBook Air Fill in the table for the probability distribution of the variable X-3. Pr(X-3=k) k -2 -1 2 00000 Clear all Check answ

Let the random variable X have the probability distribution listed in the table below. Determine the probability distribution of the random variable X-3. k 1 2 3 4 5 Pr(X=k) 0.3 0.1 View an example 0.2 0.3 0.1 Get more help - MacBook Air Fill in the table for the probability distribution of the variable X-3. Pr(X-3=k) k -2 -1 2 00000 Clear all Check answ

Advanced Engineering Mathematics
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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**Probability Distribution of a Transformed Random Variable** *Given Problem* Let the random variable \( X \) have the probability distribution as shown in the table below. Our task is to determine the probability distribution of the transformed random variable \( X - 3 \). | \( k \) | \( \Pr(X = k) \) | |---|---| | 1 | 0.3 | | 2 | 0.1 | | 3 | 0.2 | | 4 | 0.3 | | 5 | 0.1 | *Solution Approach* To find the probability distribution of \( X - 3 \), subtract 3 from each value of \( k \) and retain their corresponding probabilities. *Transformation and Table Completion* Fill in the following table for the variable \( X - 3 \): | \( k \) | \( \Pr(X - 3 = k) \) | |---|---| | -2 | 0.3 | | -1 | 0.1 | | 0 | 0.2 | | 1 | 0.3 | | 2 | 0.1 | *Process Explanation* 1. For \( k = 1 \), \( \Pr(X - 3 = -2) = 0.3 \). 2. For \( k = 2 \), \( \Pr(X - 3 = -1) = 0.1 \). 3. For \( k = 3 \), \( \Pr(X - 3 = 0) = 0.2 \). 4. For \( k = 4 \), \( \Pr(X - 3 = 1) = 0.3 \). 5. For \( k = 5 \), \( \Pr(X - 3 = 2) = 0.1 \). This transformation demonstrates how altering the random variable affects its probability distribution while preserving the total probability as 1.
Transcribed Image Text:**Probability Distribution of a Transformed Random Variable** *Given Problem* Let the random variable \( X \) have the probability distribution as shown in the table below. Our task is to determine the probability distribution of the transformed random variable \( X - 3 \). | \( k \) | \( \Pr(X = k) \) | |---|---| | 1 | 0.3 | | 2 | 0.1 | | 3 | 0.2 | | 4 | 0.3 | | 5 | 0.1 | *Solution Approach* To find the probability distribution of \( X - 3 \), subtract 3 from each value of \( k \) and retain their corresponding probabilities. *Transformation and Table Completion* Fill in the following table for the variable \( X - 3 \): | \( k \) | \( \Pr(X - 3 = k) \) | |---|---| | -2 | 0.3 | | -1 | 0.1 | | 0 | 0.2 | | 1 | 0.3 | | 2 | 0.1 | *Process Explanation* 1. For \( k = 1 \), \( \Pr(X - 3 = -2) = 0.3 \). 2. For \( k = 2 \), \( \Pr(X - 3 = -1) = 0.1 \). 3. For \( k = 3 \), \( \Pr(X - 3 = 0) = 0.2 \). 4. For \( k = 4 \), \( \Pr(X - 3 = 1) = 0.3 \). 5. For \( k = 5 \), \( \Pr(X - 3 = 2) = 0.1 \). This transformation demonstrates how altering the random variable affects its probability distribution while preserving the total probability as 1.
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