this is a question from a statistics book that i thought i solved
correctly, but my answer disagrees with the book's answer. i'd like to
find out which is the right answer. suppose that a store owner pays $1
for copies of magazines and the price it is sold to customers is $2.
suppose leftover magazines are worth $0. what can the store owner
expect to make if she orders 3 magazines?

suppose x is the demand variable, and
p(x = 1) = 1/15
p(x = 2) = 2/15
p(x = 3) = 3/15
p(x = 4) = 4/15
p(x = 5) = 3/15
p(x = 6) = 2/15

we obviously need to compute the expected value of the revenue for the
store owner when she sells 3 magazines. i use the fact that E(aX + b)
= aE(x) + b to get:

2E(x) - 3

and then:

2((1)(1/15) + (2)(2/15) + (3)(3/15) + (4)(4/15) + (5)(3/15) + (6)
(2/15)) - 3 = 4.6

my book instead does: Sum from i = 1 to 6 of h(i) * p(i) where h(i) =
2i-3, to get about 2.46. i thought the two methods were equivalent,
but they seem to give different answers. what is wrong with my
approach?

hi,

this is a question from a statistics book that i thought i solved
correctly, but my answer disagrees with the book's answer. i'd like to
find out which is the right answer. suppose that a store owner pays $1
for copies of magazines and the price it is sold to customers is $2.
suppose leftover magazines are worth $0. what can the store owner
expect to make if she orders 3 magazines?

suppose x is the demand variable, and
p(x = 1) = 1/15
p(x = 2) = 2/15
p(x = 3) = 3/15
p(x = 4) = 4/15
p(x = 5) = 3/15
p(x = 6) = 2/15

we obviously need to compute the expected value of the revenue for the
store owner when she sells 3 magazines. i use the fact that E(aX + b)
= aE(x) + b to get:

2E(x) - 3

and then:

2((1)(1/15) + (2)(2/15) + (3)(3/15) + (4)(4/15) + (5)(3/15) + (6)
(2/15)) - 3 = 4.6

my book instead does: Sum from i = 1 to 6 of h(i) * p(i) where h(i) =
2i-3, to get about 2.46. i thought the two methods were equivalent,
but they seem to give different answers. what is wrong with my
approach?

thanks.

perfreem@yahoo.com wrote:
hi,
this is a question from a statistics book that i thought i solved
correctly, but my answer disagrees with the book's answer. i'd like to
find out which is the right answer. suppose that a store owner pays $1
for copies of magazines and the price it is sold to customers is $2.
suppose leftover magazines are worth $0. what can the store owner
expect to make if she orders 3 magazines?
suppose x is the demand variable, and
p(x = 1) = 1/15
p(x = 2) = 2/15
p(x = 3) = 3/15
p(x = 4) = 4/15
p(x = 5) = 3/15
p(x = 6) = 2/15
we obviously need to compute the expected value of the revenue for
the
store owner when she sells 3 magazines. i use the fact that E(aX + b)
= aE(x) + b to get:
2E(x) - 3
and then:
2((1)(1/15) + (2)(2/15) + (3)(3/15) + (4)(4/15) + (5)(3/15) + (6)
(2/15)) - 3 = 4.6
my book instead does: Sum from i = 1 to 6 of h(i) * p(i) where h(i) =
2i-3, to get about 2.46. i thought the two methods were equivalent,
but they seem to give different answers. what is wrong with my
approach?
thanks.


Looks like a typo. SUM i=1 to 6 of (2i-3)P(x=i)=4.600