Math Problem Statement

Given the probability distributions shown to the​ right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution​ B? d. Compare the results of distributions A and B. Distribution A Distribution B

x Subscript i ​P(Xequalsx Subscript i​) x Subscript i ​P(Xequalsx Subscript i​) 0 0.06 0 0.40 1 0.12 1 0.25 2 0.17 2 0.17 3 0.25 3 0.12 4 0.40 4 0.06 Question content area bottom Part 1 a. What is the expected value for distribution​ A? muequals    enter your response here ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Probability Distributions
Expected Value
Standard Deviation

Formulas

Expected value formula: E(X) = Σ [x_i * P(X = x_i)]
Standard deviation formula: σ = sqrt(Σ [(x_i - μ)^2 * P(X = x_i)])
Probability formula: P(X ≥ x)

Theorems

Law of Large Numbers (related to expected value)
Properties of Discrete Probability Distributions

Suitable Grade Level

Grades 10-12