The daily demand for pumpkin pies at a corner grocery store is a random variable with probability mass function 1 px (k)= -{=0) 16 k for k= 0, 1, 2, 3, 4 otherwise The cost of baking one pumpkin pie is $1.00. The store sells the pies for $3.00, each. At the beginning of every day, the store manager must decide how many pies to bake. At the end of the day, any unsold pies are thrown away. If the demand for pies exceeds the supply, you can only sell those pies that you have already baked for that day. The additional customers leave unsatisfied. (a) Find P(X> 0). (b) Find E(X). (c) Find Var(X). (d) If the manager decides to bake three pies, what is the ex- pected profit for that day?
The daily demand for pumpkin pies at a corner grocery store is a random variable with probability mass function 1 px (k)= -{=0) 16 k for k= 0, 1, 2, 3, 4 otherwise The cost of baking one pumpkin pie is $1.00. The store sells the pies for $3.00, each. At the beginning of every day, the store manager must decide how many pies to bake. At the end of the day, any unsold pies are thrown away. If the demand for pies exceeds the supply, you can only sell those pies that you have already baked for that day. The additional customers leave unsatisfied. (a) Find P(X> 0). (b) Find E(X). (c) Find Var(X). (d) If the manager decides to bake three pies, what is the ex- pected profit for that day?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:The daily demand for pumpkin pies at a corner grocery store is a random
variable with probability mass function
1
4
(1)
for k= 0, 1,2,3,4
Px (k)
=
16 k
0
otherwise
The cost of baking one pumpkin pie is $1.00. The store sells the pies for
$3.00, each. At the beginning of every day, the store manager must decide
how many pies to bake. At the end of the day, any unsold pies are thrown
away. If the demand for pies exceeds the supply, you can only sell those pies
that you have already baked for that day. The additional customers leave
unsatisfied.
(a) Find P(X> 0).
(b) Find E(X).
(c) Find Var(X).
(d) If the manager decides to bake three pies, what is the ex-
pected profit for that day?
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