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Solution 3
(a) By using 2000 as the Base period, Let
P0 represents the price per kg in 2000, and
Pt represents the price per kg in 2008, and
Q0 represents the quantity in 2000, and
Qt represents the quantity in 2008, then
Laspeyres price index can be calculated as following:
Paasche price index can be calculated as following:
Fisher price index can be calculated as following:
(b) 1. Laspeyres price index chooses the base period (2000) quantity , to measure the price change degree on the condition of invariant quantity . That means if there is no quantity change, one can buy shellfish at the current wholesale price which is about 1.078702 times of the price in the base period .
2. Paassche price index chooses the current period (2008) quantity , to measure the price changing degree on the occasion of invariant current quantity . If no change is on the current quantity, the shellfish price will be 1.071991 times of the base wholesale price.
3. Fisher price index is known as “ideal” price index. Fisher price index is composed as the geometric mean of PP and PL. when measuring the price change degree, no consideration on the quantity variance, the current period price is about 1.075341 times of the base period price.
Solution 4
(a) According Poisson distribution probability formula,
,
and λ=4
The probability of exactly four people arrive at the information booth can be calculated as,
Note: In the Microsoft Excel 2003, “POISSON (4, 4, false)” can be used to get the result.
(b) Similarly as solution (a),
The probability that more than one person will arrive can be calculated as,
1-[P(x=0) + P(x=1)] =1-0.018316-0.073263=0.908422
Note: In the Microsoft Excel 2003, “POISSON (1, 4, true)” can be used to get the probability P(x>1) by using to P(x=0) and P(x=1) calculated.
(c) Similarly as solution (a) and (b), the probabilities can be calculated as following:
P(x=0) = 0.018315639
P(x=1) = 0.073262556
P(x=2) = 0.146525111
P(x=3) = 0.195366815
P(x=4) = 0.195366815
P(x=5) = 0.156293452
P(x=6) = 0.104195635
Six people arrive over a 10-minute period can be formed as follows:
abbreviation first 5-minute second 5-minute probability result
(0,6) 0 6 p(x=0)* p(x=6) 0.00190841
(1,5) 1 5 p(x=1)* p(x=5) 0.011450458
(2,4) 2 4 p(x=2)* p(x=4) 0.028626144
(3,3) 3 3 p(x=3)* p(x=3) 0.038168192
(4,2) 4 2 p(x=4)* p(x=2) 0.028626144
(5,1) 5 1 p(x=5)* p(x=1) 0.011450458
(6,0) 6 0 p(x=6)* p(x=6) 0.00190841
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