HW2

STAT 208. ASSIGNMENT NO. 10
Due on Thursday, April 10, 1997

Read Chapters 17 and 18.

Do the following exercises:

17.12

18.18: Job Sharing Data . Please describe how to do this problem. You do not have to do the actual computation.

Additional Problem: One popular model for the life time (for example the life time of light bulbs from GE) distribution is the exponential distribution, which is specified by a density function:

      f(x) =  lambda * exp{-lambda x},       for x > 0

or the corresponding cumulative distribution function:

      F(x) =   P { X <=  x  }  =  1 -  exp{-lambda x}

for some parameter lambda>0. This lambda is often unknown and has to be estimated from a data set.

(a). What is the probability that the life time is between a and b, P{ a < X <= b } ?
(b). In order to check the model validity, we draw a random sample of the life time and record the values here. Based on these data, use the Chi-square goodness of fit test to test if the model is indeed an exponential distribution with some lambda>0. [Note that the mean of an exponential random variable is 1/lambda, so a reasonable estimator of lambda is 1/xbar, the inverse of the sample mean.]