Let X is a random variable following the Negative Binomial d

Let X is a random variable following the Negative Binomial distribution with r = 3, p = 0.7. a) Find P(X<5). b) Find the mean and the variance of X.

Solution

a)

b*(x; r, P) = _x-1C_r-1 * P^r * (1 - P)^{x - r}

P(X<5) = P(X=3) + P(X=4)

= 2C2 * (0.7)^3 * (0.3)^0 + 3C2 * (0.7)^3 * (0.3)^1

= (0.7)^3 + 3 * (0.7)^3 * (0.3)^1

= 0.65 Answer

b)

Mean = r/P = 3 /0.7 = 4.285

Variance = rq/P² = (3* 0.3)/(0.7*0.7) = 1.836