. Test at the 10% significance level the hypothesis that the following data

06.88 06.92 04.80 09.85 07.05 19.06 06.54 03.67 02.94 04.89

69.82 06.97 04.34 13.45 05.74 10.07 16.91 07.47 05.04 07.97

15.74 00.32 04.14 05.19 18.69 02.45 23.69 44.10 01.70 02.14

05.79 03.02 09.87 02.44 18.99 18.90 05.42 01.54 01.55 20.99

07.99 05.38 02.36 09.66 00.97 04.82 10.43 15.06 00.49 02.81

give the values of a random sample of size 50 from an exponential distribution with probability density function

1 e x

if 0 < x <

where > 0.

2)

Let X1, X2, ..., X10 be a random sample from a distribution whose probability density function is

f (x) =1 if 0

&

0 otherwise

0 otherwise.

Based on the observed values 0.62, 0.36, 0.23, 0.76, 0.65, 0.09, 0.55, 0.26, 0.38, 0.24, test the hypothesis Ho : X UNIF (0, 1) against Ha : X / UNIF (0, 1) at a significance level = 0.1.