Contribution to E(X)

• 50 total items, 20 are successes (40%). Draw 10? Expect 4.00 successes
• Like drawing cards without replacement - each draw affects the next
• Typical range: 3 to 5 successes

What Does E(X) Mean?

The expected value E(X) represents the average number of successes you will get when drawing n items without replacement from a population of N items containing K successes. It is the proportion of successes in the population multiplied by your sample size.

Interpreting Your Result

With E(X) = 4.00, this means:

• Expect 4.00 successes in your sample of 10
• Population has 40.0% success rate
• No replacement: each draw changes the remaining population slightly

Real-World Examples

• Card games: 52 cards, 13 hearts, draw 5? Expect 1.25 hearts
• Quality control: 100 items, 10 defective, sample 20? Expect 2 defects
• Lottery: 50 balls, 20 winning, draw 10? Expect 4 winners

Why E(X) = n × K / N

This formula reflects the simple fact that your sample should reflect the population proportion. If K/N of the population are successes, then K/N of your sample should be successes too. Multiply by n to get the count: n × (K/N) = nK/N. Unlike binomial, there is no replacement, but the expected value is the same - it is the variance that differs!