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 P(X=x) 0 U alo X

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**Transcription for Educational Website**

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 \( thh \), then \( N (thh) = 1 \). Suppose that the random variable \( X \) is defined in terms of \( N \) as follows: 

\[
X = N - N^2 - 4
\]

The values of \( X \) are given in the table below.

\[
\begin{array}{|c|c|}
\hline
\text{Outcome} & \text{Value of } X \\
\hline
hth & -4 \\
htt & -6 \\
tht & -6 \\
hhh & -4 \\
thh & -4 \\
ttt & -10 \\
hht & -4 \\
tth & -6 \\
\hline
\end{array}
\]

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.

\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Value } x \text{ of } X & & & & \\
\hline
p(X = x) & & & & \\
\hline
\end{array}
\]

The table below is intended for you to input the possible values of \( X \) and the corresponding probabilities of each value. Use the 'Check' button to verify your answers.

*(Buttons: Save For Later, Submit Assignment)*

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Transcribed Image Text:**Transcription for Educational Website** 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 \( thh \), then \( N (thh) = 1 \). Suppose that the random variable \( X \) is defined in terms of \( N \) as follows: \[ X = N - N^2 - 4 \] The values of \( X \) are given in the table below. \[ \begin{array}{|c|c|} \hline \text{Outcome} & \text{Value of } X \\ \hline hth & -4 \\ htt & -6 \\ tht & -6 \\ hhh & -4 \\ thh & -4 \\ ttt & -10 \\ hht & -4 \\ tth & -6 \\ \hline \end{array} \] 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. \[ \begin{array}{|c|c|c|c|c|} \hline \text{Value } x \text{ of } X & & & & \\ \hline p(X = x) & & & & \\ \hline \end{array} \] The table below is intended for you to input the possible values of \( X \) and the corresponding probabilities of each value. Use the 'Check' button to verify your answers. *(Buttons: Save For Later, Submit Assignment)* © 2023 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center
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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 thh, then N (thh)= 1. Suppose that the random variable X is defined in terms of N as follows: X = N-N2 - 4. The values of X are given in the table.

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