I. An urn contains five balls numbered 1,2,3,4,5. A ball is drawn at random. Let $X$ be the number shown on the ball. This ball is replaced. Then 200 balls are drawn, one at a time, with replacement. Let $Y$ be the sum of the numbers on the 200 balls. Let $Z$ be the average $g^{f}$ the numbers on the 200 balls. Find
3)
3) $E(Y)$
Choices
Answer
Final Answer: \( \boxed{600} \)
Step 1 ：Calculate the expected value of a single draw, \( E(X) \), which is the average of the numbers on the balls
Step 2 ：Since each number has an equal probability of being drawn, \( E(X) = \frac{1+2+3+4+5}{5} = 3 \)
Step 3 ：Find the expected value of \( Y \), which is the sum of the numbers on the 200 balls, by multiplying the expected value of a single draw by the number of draws
Step 4 ：\( E(Y) = E(X) \times 200 = 3 \times 200 = 600 \)
Step 5 ：Final Answer: \( \boxed{600} \)
