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

\

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

• 7.5
• 1
• 8.7
• 0.25

Explanation:

Define the expected value formula

$$ E(X) = \sum x_i \cdot P(x_i) $$

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 expected value

$$
LATEXBLOCK0
$$

Answer:

• (A) 7.5
• (B) 1
• (C) 8.7 (Correct answer)
• (D) 0.25