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Expected Value Calculations

This document contains examples and explanations of concepts related to expected value and probability. Table 5-3 shows the calculation of expected value using frequency and relative frequency for patient numbers and categories. Table 5-6 calculates expected losses for different levels of stock using possible sales amounts, conditional losses, and probabilities of each sale amount. It determines the best stock option has the lowest expected loss. Self Check 5-3 similarly calculates expected losses for different levels of pizza stock to determine the best option.

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47 views6 pages

Expected Value Calculations

This document contains examples and explanations of concepts related to expected value and probability. Table 5-3 shows the calculation of expected value using frequency and relative frequency for patient numbers and categories. Table 5-6 calculates expected losses for different levels of stock using possible sales amounts, conditional losses, and probabilities of each sale amount. It determines the best stock option has the lowest expected loss. Self Check 5-3 similarly calculates expected losses for different levels of pizza stock to determine the best option.

Uploaded by

Npranto
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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page 226

Expected value of a discrete random variable

table 5-3

1 2 3 4 5 (1*3)
N. of Pat. Freq (X) RF (X/Sum X) Freq * RF Cat. * RF add +
100 1 0.01 0.01 1.00 deduct -
101 2 0.02 0.04 2.02 multiply *
102 3 0.03 0.09 3.06 divide /
103 5 0.05 0.25 5.15
104 6 0.06 0.36 6.24
105 7 0.07 0.49 7.35
106 9 0.09 0.81 9.54
107 10 0.10 1.00 10.70
108 12 0.12 1.44 12.96
109 11 0.11 1.21 11.99
110 9 0.09 0.81 9.90
111 8 0.08 0.64 8.88
112 6 0.06 0.36 6.72
113 5 0.05 0.25 5.65
114 4 0.04 0.16 4.56
115 2 0.02 0.04 2.30
Sum X 100 1 108.02
page 229

Self Check

SC 5-1

1 2 3 4 (1*3)
Outcome Freq (X) RF (X/Sum X) Outcome*RF
102 10 0.08 8.16
105 20 0.16 16.80
108 45 0.36 38.88
111 15 0.12 13.32
114 20 0.16 18.24
117 15 0.12 14.04
Sum X 125 1.00 109.44 (Expected Value)
Page 233

Types of losses:

Wastage / Obsolescence Loss

Opportunity Loss

Table 5-6
Daily Sales N. of Days RF Prob.
10 15 0.15 Purchasing price / box= 20$
11 20 0.20 Selling price / box = 50$
12 40 0.40 Profit / box = 30$
13 25 0.25 Wastage loss= 20$
Total days= 100 1.00 Opportunity loss= 30$

Possible stock
Possible Sales 10 11 12 13 Conditional loss
10 0 20 40 60
11 30 0 20 40
12 60 30 0 20
13 90 60 30 0

For stock of 10 box


Possible sales Conditional L. Pr. Of Sales CL * Pr.
10 0 0.15 0.00
11 30 0.20 6.00
12 60 0.40 24.00
13 90 0.25 22.50
Expected L. 52.50

For stock of 11 box


Possible sales Conditional L. Pr. Of Sales CL * Pr.
10 20 0.15 3.00
11 0 0.20 0.00
12 30 0.40 12.00
13 60 0.25 15.00
Expected L. 30.00

For stock of 12 box


Possible sales Conditional L. Pr. Of Sales CL * Pr.
10 40 0.15 6.00
11 20 0.20 4.00
12 0 0.40 0.00
13 30 0.25 7.50
Expected L. 17.50

For stock of 13 box


Possible sales Conditional L. Pr. Of Sales CL * Pr.
10 60 0.15 9.00
11 40 0.20 8.00
12 20 0.40 8.00
13 0 0.25 0.00
Expected L. 25.00

Possible Stock 10 11 12 13
Expected L. 52.50 30.00 17.50 25.00
Best Stock Option
Page 235
SC 5-3

Daily Sales N. of Days RF Prob.


1 0.40 Purchasing price / box= 7$
2 0.30 Selling price / box = 12$
3 0.20 Profit / box = 5$
4 0.10 Wastage loss= 7$
Total days= 0 1.00 Opportunity loss= 5$

Possible stock
Possible Sales 1 2 3 4 Conditional loss
1 0 7 14 21
2 5 0 7 14
3 10 5 0 7
4 15 10 5 0

For stock of 1 pizza


Possible sales Conditional L. Pr. Of Sales CL * Pr.
1 0 0.40 0.00
2 5 0.30 1.50
3 10 0.20 2.00
4 15 0.10 1.50
Expected L. 5.00

For stock of 2 pizza


Possible sales Conditional L. Pr. Of Sales CL * Pr.
1 7 0.40 2.80
2 0 0.30 0.00
3 5 0.20 1.00
4 10 0.10 1.00
Expected L. 4.80

For stock of 3 pizza


Possible sales Conditional L. Pr. Of Sales CL * Pr.
1 14 0.40 5.60
2 7 0.30 2.10
3 0 0.20 0.00
4 5 0.10 0.50
Expected L. 8.20

For stock of 4 pizza


Possible sales Conditional L. Pr. Of Sales CL * Pr.
1 21 0.40 8.40
2 14 0.30 4.20
3 7 0.20 1.40
4 0 0.10 0.00
Expected L. 14.00

Possible Stock 1 2 3 4
Expected L. 5.00 4.80 8.20 14.00
Best Stock Option

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