There are 1000 households in a town. Specifically, there are 100 households with one member, 200 housholds with 2 memeber, 300 households with 3 members, 200 households with 4 members, 100 households with 5 members and 100 households with 6 members. Thus, the total number of people living in the town is:N = 100 * 1 + 200 *2 + 300 * 3 + 200 * 4 + 100 * 5 + 100 * 6 = 3300. a. We pick a household at random, and define the random variable X as the number of people in the chosen household. Find the PMF and the expected value of X
b. We pick a person in the town at random, and define the random variable Y as the number of people in the household where the chosen person lives. Find the PMF and the expected value of Y

a

Expected value  

b

Expected value

Step-by-step explanation:

From question we are told that

The number of households is n = 1000

The number of households with one member is m = 100

The number of households with two member is o = 200

The number of households with three member is p = 300

The number of households with four member is q = 200

The number of households with five member is r = 100

The number of households with six member is r = 100

The total number of people living in the town is N = 3300

Generally the PMF is mathematically represented as

Here X is the random variable as defined in the question

Generally the expected value of X is mathematically represented as

=>

Considering B

Generally the PMF is mathematically represented as

Generally the expected value of Y is mathematically represented as

=>