Question

there are 4 different numbers in a hat, with many duplicates of each number. the probability distribution for each number is below. calculate the expected value.

number and probability
\

$$\begin{tabular}{|c|c|} \\hline number & probability \\\\ \\hline 3 & 0.1 \\\\ \\hline 6 & 0.25 \\\\ \\hline 9 & 0.3 \\\\ \\hline 12 & 0.35 \\\\ \\hline \\end{tabular}$$

Explanation:

State the expected value formula

$$ E(X) = \sum [x \cdot P(x)] $$

Substitute the given values into the formula

$$ E(X) = (3 \cdot 0.1) + (6 \cdot 0.25) + (9 \cdot 0.3) + (12 \cdot 0.35) $$

Calculate the final sum

$$
LATEXBLOCK0
$$

Answer:

\(8.7\)