Questions: Complete the table below. (hatp) (hatmathbfq=mathbf1-hatmathbfp) (hatmathbfp q) --- --- --- 0.6 0.7 0.8 0.9 1.0 (Type integers or decimals.)

Transcript text: Complete the table below. \begin{tabular}{|c|c|c|} \hline$\hat{p}$ & $\hat{\mathbf{q}}=\mathbf{1}-\hat{\mathbf{p}}$ & $\hat{\mathbf{p q}}$ \\ \hline 0.6 & $\square$ & $\square$ \\ \hline 0.7 & $\square$ & $\square$ \\ \hline 0.8 & $\square$ & $\square$ \\ \hline 0.9 & $\square$ & $\square$ \\ \hline 1.0 & $\square$ & $\square$ \\ \hline \end{tabular} (Type integers or decimals.)

Solution

Solution Steps

To complete the table, we need to calculate two values for each given $\hat{p}$:

$\hat{\mathbf{q}} = 1 - \hat{\mathbf{p}}$
$\hat{\mathbf{p q}} = \hat{\mathbf{p}} \times \hat{\mathbf{q}}$

We will iterate through the given $\hat{p}$ values, compute $\hat{\mathbf{q}}$ and $\hat{\mathbf{p q}}$, and then fill in the table.

Step 1: Calculate $\hat{\mathbf{q}}$

For each value of $\hat{p}$, we compute $\hat{\mathbf{q}} = 1 - \hat{\mathbf{p}}$:

For $\hat{p} = 0.6$: \[ \hat{\mathbf{q}} = 1 - 0.6 = 0.4 \]
For $\hat{p} = 0.7$: \[ \hat{\mathbf{q}} = 1 - 0.7 = 0.3 \]
For $\hat{p} = 0.8$: \[ \hat{\mathbf{q}} = 1 - 0.8 = 0.2 \]
For $\hat{p} = 0.9$: \[ \hat{\mathbf{q}} = 1 - 0.9 = 0.1 \]
For $\hat{p} = 1.0$: \[ \hat{\mathbf{q}} = 1 - 1.0 = 0.0 \]

Step 2: Calculate $\hat{\mathbf{p q}}$

Next, we compute $\hat{\mathbf{p q}} = \hat{\mathbf{p}} \times \hat{\mathbf{q}}$:

For $\hat{p} = 0.6$: \[ \hat{\mathbf{p q}} = 0.6 \times 0.4 = 0.24 \]
For $\hat{p} = 0.7$: \[ \hat{\mathbf{p q}} = 0.7 \times 0.3 = 0.21 \]
For $\hat{p} = 0.8$: \[ \hat{\mathbf{p q}} = 0.8 \times 0.2 = 0.16 \]
For $\hat{p} = 0.9$: \[ \hat{\mathbf{p q}} = 0.9 \times 0.1 = 0.09 \]
For $\hat{p} = 1.0$: \[ \hat{\mathbf{p q}} = 1.0 \times 0.0 = 0.0 \]

Final Answer

The completed table is as follows:

\[ \begin{array}{|c|c|c|} \hline \hat{p} & \hat{\mathbf{q}} & \hat{\mathbf{p q}} \\ \hline 0.6 & 0.4 & 0.24 \\ 0.7 & 0.3 & 0.21 \\ 0.8 & 0.2 & 0.16 \\ 0.9 & 0.1 & 0.09 \\ 1.0 & 0.0 & 0.0 \\ \hline \end{array} \]

Thus, the values are:

For $\hat{p} = 0.6$: $\hat{\mathbf{q}} = 0.4$, $\hat{\mathbf{p q}} = 0.24$
For $\hat{p} = 0.7$: $\hat{\mathbf{q}} = 0.3$, $\hat{\mathbf{p q}} = 0.21$
For $\hat{p} = 0.8$: $\hat{\mathbf{q}} = 0.2$, $\hat{\mathbf{p q}} = 0.16$

The final answer is: \[ \boxed{ \begin{array}{|c|c|c|} \hline \hat{p} & \hat{\mathbf{q}} & \hat{\mathbf{p q}} \\ \hline 0.6 & 0.4 & 0.24 \\ 0.7 & 0.3 & 0.21 \\ 0.8 & 0.2 & 0.16 \\ \hline \end{array} } \]

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