Math Problem Statement

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Random Variables and Distributions Discrete probability distribution: Word problems Topic Progress 0 of 5 0/5

Dennis

Problem PageQuestion An number cube (a fair die) is rolled 3 times. For each roll, we are interested in whether the roll comes up even or odd. An outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). For each outcome, let N be the random variable counting the number of even rolls in each outcome. For example, if the outcome is eoe, then =Neoe2. Suppose that the random variable X is defined in terms of N as follows: =X−2N2−4N3. The values of X are given in the table below. Outcome eeo ooe oee eee eoe eoo oeo ooo Value of X −3 −5 −3 3 −3 −5 −5 −3 Calculate the probabilities P=Xx of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P=Xx

Explanation

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Math Problem Analysis

Mathematical Concepts

Probability Distribution
Discrete Random Variables
Combinatorics

Formulas

X = -2N^2 - 4N + 3
Probability of an event P(X = x) = (number of favorable outcomes / total outcomes)

Theorems

Fundamental Principle of Counting
Discrete Probability Distributions

Suitable Grade Level

Grades 10-12