A box contains four 75 W lightbulbs, three 60 W lightbulbs, and three burned-out lightbulbs. Two bulbs are selected at random from the box without replacement. Let X represent the number of 75 W bulbs selected. Find the probability mass function for X. Show that X follows a valid probability mass function.

a. Find P (X > 0)

b. Find μx

c. Find σx^2

a. 0.689

b. 0.8

c. 0.427

Step-by-step explanation:

The given scenario indicates hyper-geometric experiment because because successive trials are dependent and probability of success changes on each trial.

The probability mass function for hyper-geometric distribution is

P (X=x) = kCx (N-k) C (n-x) / NCn

where N=4+3+3=10

n=2

k=4

a.

P (X>0) = 1-P (X=0)

The probability mass function for hyper-geometric distribution is

P (X=x) = kCx (N-k) C (n-x) / NCn

P (X=0) = 4C0 (6C2) / 10C2=15/45=0.311

P (X>0) = 1-P (X=0) = 1-0.311=0.689

P (X>0) = 0.689

b.

The mean of hyper-geometric distribution is

μx=nk/N

μx=2*4/10=8/10=0.8

c.

The variance of hyper-geometric distribution is

σx²=nk (N-k). (N-n) / N² (N-1)

σx²=2*4 (10-4). (10-2) / 10²*9

σx²=8*6*8/900=384/900=0.427