Since are constants, they can be taken out of the summation in the second and third terms. Also, note that
which proves the assertion.
The relation is important and useful since it gives us the variance directly in terms of and . You are urged to try using this relation to calculate variance in the examples of variance we’ve discussed earlier.
Two cards are drawn simultaneously from a well-shuffled deck of cards. Find the mean and variance of the number of kings.
The number of kings is the random variable here. Call it . The values that can take are , , . The probabilities of the various values are easily calculated: