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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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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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?
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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