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Question 1 (40 pts) 5.0909 1.3371 13.5739 13.5765 36.8361 30.5131 7.30876 19.9367 0.541946 7.4161613.0638 14.5477 0.782948 35.5807 5.05287 35.6135 22.6779 41.4081 18.5774 49.7615 5.4278 8.00431 17.0105 22.5901 34.924 1 Use chi-square test to test the hypothesis that the data given above follows an exponential distribution. Let the level of significance a 0.05. Some of the Chi-Square critical values: x005,3-7.82, χ20.05,,-5.99, χ005,1-3.84 Note that the probability density function and the cumulative distribution function of an exponentially distributed random variable X with the parameter A are given as follows 1-c, 0 for x 20 otherwise f(r) F(x)- 0, otherwise a) b) Use five equal probability intervals Use the following intervals [o,5) [11, 20) [20, )

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Answer #1

a)

Class Interval Observed Frequency (O) Probability (P) Expected Frequency (E )=25*P (O-E)^2/E
0 10 8 0.41198 10.299584 0.513427
10 20 8 0.24225 6.0563267 0.623788
20 30 2 0.14245 3.561221 0.684431
30 40 5 0.08376 2.0940573 4.032604
40 50 2 0.04925 1.2313406 0.479833
25 6.334083

b)

Class Interval Observed Frequency (O) Probability (P) Expected Frequency (E )=25*P (O-E)^2/E
0 5 3 0.23317756 5.8294389 1.373327
5 11 5 0.20921496 5.230374 0.010147
11 20 8 0.21184389 5.2960973 1.380467
20 infinity 9 0.34576359 8.6440898 0.014654
25 2.778595

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