1. Uniform Distribution Part 2 Intermediate and Advanced Topics Continuous Probability Distributions Uniform Probability Distribution- Introduction Uniform Probability Distribution- Example

2. The News Vendor Problem
Swell Productions is sponsoring an outdoor conclave for owners of collectible and classic Fords. The concession stand in the T-Bird area will sell clothing such as official Thunderbird racing jerseys. Suppose the probability of jerseys sales quantities is uniformly (and continuously) distributed between 100 and Suppose sales price is $80 per jersey, purchase cost is $40, and unsold jerseys are returned to the manufacturer for $20 per unit. How many Jerseys Swell Production orders?
100
400
Cu: Underage Cost
Cu = = 40
Co: Overage Cost Q
If Co was also 40 40 40
Gray /(White + Gray)
Cu/(Cu+Cp) = 40/(40+40) = 0.5 20 40
Co = = 20
 40/(20+60) =2/3

3. The News Vendor Problem
SL* = Cu/(Cu+Co)
SL* = 40/(40+20) = 2/3
(Q-100)/( ) = 2/3
Q= 300
100
400 Q

4. The News Vendor Problem
The expected number of participants in a conference is uniformly distributed between 100 and The participants spend one night in the hotel and the cost is paid by the conference. The hotel has offered a rate of $200 per room if a block of rooms is reserved (non-refundable) in advance. The rate in the conference day is $300. All rooms will be single occupied. How many rooms should we reserve in the non-refundable block to minimize our expected total cost.
Service level (Probability of demand not exceeding what we have ordered) SL* = Cu/(Cu+Co)
Co: Overage cost
Co = 200.
Cu: Underage cost
Cu = = 100
100
700

5. The News Vendor Problem
SL* = Cu/(Cu+Co)
SL* = 100/( ) = 1/3
SL* = (Q-a)/(b-a) = (Q-100)/600 = 1/3 ?
1/600
0.3333
a=100
b=700
Q= 300
B-a=600

6. A Non-Trivial Problem – Curve, Solver, Data table
Profit = (12-x)
E(Profit) = 0.2(x-4)(12-x)
E(profit) = -0.2x2+3.2x-9.6
x = price offered.
Probability of wining = 0.2(x-4)

7. Estimating the Demand Curve

8. Estimating the Demand Curve

9. From Economics to Statistics
160
a= 0, b= 160
f(x) =1/160
µ= (0+160)/2
σ2 = (160-0)2/12
If price is set to P, probability of sale is 1/160(160-P) = 1-P/160
160 P
What Price maximizes our revenue?
If V= 75, What Price maximizes our profit?

10. From Uniform Dist. to Binomial Distribution
If price is set to P, probability of sale is 1-P/160
Probability of not sale is 1-(1-P/160)= P/160
If 200 people visit this site, what is average sales?
What is standard deviation of sales?