Suppose that the time to death in days of a newly formed red blood cell follows the distribution above with

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. If the hazard rate of x is h(x) = λ   λ > 0, determine the survival function of x.

2. Suppose that the time to death in days of a newly formed red blood cell follows the distribution above with λ = 1/120 , find;

(a) The probability that a randomly chosen newly formed red blood cell will die within the first 4 weeks.

(b) The probability that a randomly chosen newly formed red blood cell will die within a week after surviving 5 weeks.

(c) The median time to death of a newly formed red blood cell.

3. Verify that if T has a Weibull distribution, then log T has an extreme-value distribution.

4. The following data gives the remission times (in weeks) of treated Leukemia

patients,

             6,6,6,6,6,7,9,10,10,11,13,16,17,19,20,22,23,25,32,32,34,35.

Find the Maximum Likelihood Estimate of the parameters when fitting the Weibull distribution.

5. Let T1, T2, . . . , Tn be independent random variables with Weibull distribution with scale parameters ρ1, ρ2, . . . , ρn and common index k. Find the survivor function of T = min(T1, T2, . . . Tn).

6. The following data gives the remission times (in weeks) of treated leukemia patients;

      6*,6,6,6,6,7,9*,10*,10,11*,13,16,17*,19*,20*,22,23,25*,32*,34*,35*.

Find the Maximum Likelihood Estimate of the parameters when fitting the Weibull distribution.

7. The following table lists 42 times to remission of a disease, half from patients receiving no treatment (control) and half receiving the drug 6.MP. The remission times are in weeks, and those censored are indicated with a +;

 

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