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Find the expected value of the random variable. X 2 3 4 5 P(x) 0.1 0.3 0.1 0.5

Find the expected value of the random variable. X 2 3 4 5 P(x) 0.1 0.3 0.1 0.5

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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**Find the Expected Value of the Random Variable** The table below provides the values of a discrete random variable \( x \) and their corresponding probabilities \( P(x) \). | \( x \) | 2 | 3 | 4 | 5 | |-----------|----|----|----|----| | \( P(x) \) | 0.1 | 0.3 | 0.1 | 0.5 | **What is the expected value?** (Type an integer or a decimal.) --- To find the expected value \( E(x) \), use the formula: \[ E(x) = \sum [x \cdot P(x)] \] 1. Calculate for each value of \( x \): - \( 2 \cdot 0.1 = 0.2 \) - \( 3 \cdot 0.3 = 0.9 \) - \( 4 \cdot 0.1 = 0.4 \) - \( 5 \cdot 0.5 = 2.5 \) 2. Sum these results: - \( 0.2 + 0.9 + 0.4 + 2.5 = 4.0 \) **Expected Value: 4.0**
Transcribed Image Text:**Find the Expected Value of the Random Variable** The table below provides the values of a discrete random variable \( x \) and their corresponding probabilities \( P(x) \). | \( x \) | 2 | 3 | 4 | 5 | |-----------|----|----|----|----| | \( P(x) \) | 0.1 | 0.3 | 0.1 | 0.5 | **What is the expected value?** (Type an integer or a decimal.) --- To find the expected value \( E(x) \), use the formula: \[ E(x) = \sum [x \cdot P(x)] \] 1. Calculate for each value of \( x \): - \( 2 \cdot 0.1 = 0.2 \) - \( 3 \cdot 0.3 = 0.9 \) - \( 4 \cdot 0.1 = 0.4 \) - \( 5 \cdot 0.5 = 2.5 \) 2. Sum these results: - \( 0.2 + 0.9 + 0.4 + 2.5 = 4.0 \) **Expected Value: 4.0**
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