3 Suppose we toss a coin. Successive coin tosses are independent and yield heads with probability p. The negative binomial random variable with parameter k assumes a value n if it takes n failures until the kth success occurs. Use z-transforms to determine the probability mass function for the negative binomial random variable.

Hint: The number of ways of making k choices from the numbers 0, 1, . . . , n add up to n is given by

Transcribed Image Text:

(n + k 1)! n!(k-1)!