Math Problem Statement

The probability distribution of the random variable X is given in the following table. Find the standard deviation of the random variable X. (Round your answer to 4 decimal places.) 

x

1

2

3

4

5

P(X =x)

0.29

0.22

0.13

0.16

0.2

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Distribution
Random Variables
Mean (Expected Value)
Variance
Standard Deviation

Formulas

Mean (\( \mu \)): \( \mu = \sum_{x} x \cdot P(X = x) \)
Variance (\( \sigma^2 \)): \( \sigma^2 = \sum_{x} P(X = x) \cdot (x - \mu)^2 \)
Standard Deviation (\( \sigma \)): \( \sigma = \sqrt{\sigma^2} \)

Theorems

Law of Total Probability
Properties of Variance

Suitable Grade Level

Grades 10-12