Pls help Math questions

用戶43944

2012-12-05 6:56 am

A businessman evaluated his chance of obtaining a contract to produce 1,000, 1,500, 2,000, 2,500 or 3,000 pairs of shoes as follows:

Number of pairs (probability) 1,000 (16k) 1,500 (8k) 2,000 (4k) 2,500 (2k) 3,000(k)

a Find the value of k, the chance of producing 3,000 pairs of shoes in one contract
b What are the expectation and standard deviation of pairs of shoes to be produced in one contract?

回答 (1)

用戶25975

2012-12-05 7:24 am

✔ 最佳答案

a) From the given we have:

16k + 8k + 4k + 2k + k = 1

31k = 1

k = 1/31

which is also the probability of producing 3000 pairs of shoes.

b) E(X) = 1000 x 16/31 + 1500 x 8/31 + 2000 x 4/31 + 2500 x 2/31 + 3000 x 1/31

= 40000/31

E(X2) = 10002 x 16/31 + 15002 x 8/31 + 20002 x 4/31 + 25002 x 2/31 + 30002 x 1/31

= 71500000/31

Hence variance is:

E(X2) - [E(X)]2 = 641519

With standard deviation = 801 (corr. to the nearest integer)

2012-12-05 09:00:13 補充：
c) expected revenue gain = 200 x 40000/31 = $258065
standard deviation = √200 x 801 = $11328

d) expected revenue gain = 10 x 258065 = $2580650
standard deviation = √10 x 11328 = $35822

參考: 原創答案

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