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
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