Math Problem Statement

Determine the mean and variance of the random variable X given its probability distribution: x = {0,1,2,3,4,5,6,7,8} and P(X=x) = {0.1366, 0.3142, 0.0469, 0.0785, 0.0636, 0.0785, 0.0455, 0.0791, 0.1571}.

Solution

The mean and variance of the random variable XX are:

  • (a) Mean = 3.37
  • (b) Variance = 8.37

Would you like further details or have any questions? Here are 5 related questions for further understanding:

  1. How do you calculate the expected value of a discrete random variable?
  2. What is the relationship between the mean and variance of a probability distribution?
  3. Can the variance ever be negative? Why or why not?
  4. How would the mean and variance change if the probabilities in the distribution were different?
  5. How does variance affect the spread of a distribution?

Tip: The variance measures how much the values of the random variable deviate from the mean on average. A higher variance indicates a wider spread in the data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability Distributions
Expected Value
Variance

Formulas

Mean (Expected Value): E(X) = Σ[x * P(X=x)]
Variance: Var(X) = Σ[(x - E(X))^2 * P(X=x)]

Theorems

Law of Total Expectation
Properties of Variance

Suitable Grade Level

Grades 10-12

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