The gamma density function for a random variable Y is The montly salary of women

Question

The gamma density function for a random variable Y is

The montly salary of women that are in the labor force in a large town, Y, follows a gamma distribution with =2000 and =4. The city is planning to obtain a random sample of 100 women to obtain some information. The city is planning to ask the 100 women about their salary.

Let y1,y2,...,y100 represent the salary of these women. Consider the random variable

The expected value of W is  

Select one:

a. 500

b. 5000

c. 1000

d. 2000

e. 3000

Explanation / Answer

as expected value of gamma distribution y=/ =2000/4=500

hence expected value of w=4*100*E(Y)/100=4*500=2000

hence option d

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