Question

Let ? be the number of participants in a random meeting. The probability mass function of ? is given below. Assume that the meetings are independent.

0.5 for ? = 2

?(?) = 0.2 for ? = 4

0.3 for ? = 8

a) Find the mean and variance of ?.

b) What is the probability that the total number of participants in two meetings is exactly 10?

c) What is the probability that the number of participants in one meeting is fewer than 5?

d) What is the probability that the average number of participants in ten meetings is fewer than 5?

e) What is the probability that at least two out of ten meetings have less than 5 participants?

Answer 1

a)

Mean =

Also,

So,

b)

Let X1 and X2 denote the number of participants in 1st and 2nd meeting respectively.

Required probability =

c)

Required probability =

d)

Using Normal approximation,

Using Central Limit theorem, we know,

Required probability =

e)

Let Y denote the number of meeting that have fewer than 5 participants.

Then

Required probability =