Question

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 odd rolls in each outcome. For example, if the outcome is eoe, then \( N(e o e)=1 \). Suppose that the random variable \( X \) is defined in terms of \( N \) as follows: \( X=2 N^{2}-2 N-3 \). The values of \( X \) are given in the table below. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline Outcome & oee oeo ooe eoe ooo eoo eeo eee \\ Value of \( \boldsymbol{x} \) & -3 & 1 & 1 & -3 & 9 & 1 & -3 & -3 \\ \hline \end{tabular} Calculate the probabilities \( P(X=x) \) 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 \( x \) Explanation Pecheck

          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 odd rolls in each outcome. For example, if the outcome is eoe, then \( N(e o e)=1 \). Suppose that the random variable \( X \) is defined in terms of \( N \) as follows: \( X=2 N^{2}-2 N-3 \). The values of \( X \) are given in the table below.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline Outcome & oee oeo ooe eoe ooo eoo eeo eee \\
Value of \( \boldsymbol{x} \) & -3 & 1 & 1 & -3 & 9 & 1 & -3 & -3 \\
\hline
\end{tabular}

Calculate the probabilities \( P(X=x) \) 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 \( x \)
Explanation
Pecheck

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 odd rolls in each outcome. For example, if the outcome is eoe, then N(e o e)=1. Suppose that the random variable X is defined in terms of N as follows: X=2 N^2-2 N-3. The values of X are given in the table below.

Outcome oee oeo ooe eoe ooo eoo eeo eee

Value of x -3 1 1 -3 9 1 -3 -3

Calculate the probabilities P(X=x) 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
Explanation
Pecheck

Added by Linda B.

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