In this problem, our goal is to find the variance of the hypergeometric distribution. Let's remember the random experiment behind the hypergeometric distribution. You have a bag that contains b blue marbles and r red marbles. You choose k ≤ b + r marbles at random (without replacement) and let X be the number of blue marbles in your sample. Then X ∼ Hypergeometric (b, r, k). Now let us define the indicator random variables X_i as follows.

Then, we can write

Using the above equation, show

Transcribed Image Text:

:{} 0 X₁ = = if the ith chosen marble is blue otherwise