Question

People visiting video rental stores often rent more than one DVD at a time. The probability distribution for DVD rentals per customer at Video To Go is given below. There is a five-video limit per customer at this store, so nobody ever rents more than five DVDs.

Video To Go
x	0	1	2	3	4	5
P(X = x)	0.04	0.53	0.24	?	0.06	0.04

Another shop, Entertainment Headquarters, rents DVDs and videogames. The probability distribution for DVD rentals per customer at this shop is given below. They also have a five DVD limit per customer.

Entertainment Headquarters
x	0	1	2	3	4	5
P(X = x)	0.35	0.25	0.2	0.1	0.05	0.05

If Video to Go estimates that they will have 300 customers next week, how many DVDs do they expect to rent next week?
DVDs

Entertainment Headquarters projects that they will have 420 customers next week. How many DVDs do they expect to rent next week?
  DVDs

For which store is the expected number of DVD rentals for next week higher?

Entertainment HeadquartersVideo To Go   

Answer 1

1) for  Video to Go expected DVD;s rented per customer = $\sum xP(x)$

=0*0.04+1*0.53+2*0.24+3*0.09+4*0.06+5*0.04 =1.72

hence expected DVD's  Video to Go estimates to rent for 300 customers =300*1.72=516

2)

for  Entertainment Headquarters expected DVD;s rented per customer = $\sum xP(x)$

=0*0.35+1*0.25+2*0.2+3*0.1+4*0.05+5*0.05 =1.4

hence expected DVD's  Entertainment Headquarters estimates to rent for 420 customers =420*1.4=588

Entertainment Headquarters expected to rent higher number of DVD's