Math Problem Statement

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is tht, then =Ntht2. Suppose that the random variable X is defined in terms of N as follows: =X−N2−N4. The values of X are given in the table below. Outcome tth hth thh tht hht htt ttt hhh Value of X −2 −4 −4 −2 −4 −2 2 −4 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

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Random Variables
Discrete Probability Distribution

Formulas

Probability P(X = x) = Frequency of X / Total Outcomes
X = -N^2 - N^4

Theorems

Law of Total Probability
Concept of Expected Value

Suitable Grade Level

Grades 9-12