survival distribution of a group of patients

(i) Suppose that the survival distribution of a group of patients follows theexponential distribution with G = 0 (year),λ = 0.65. Plot the survivorshipfunction and find:

(a) The mean survival time

(b) The median survival time

(c) The probability of surviving 1.5 years or more

(ii) Suppose that the survival distribution of a group of patients follows theexponential distribution with G = 5 (years) and λ = 0.25. Plot the survivorshipfunction and find:

(a) The mean survival time

(b) The median survival time

(c) The probability of surviving 6 years or more

(iii) Consider the following two we bull distributions as survival models:

(i) G = 0,  1, γ= 0.5

(ii) G = 0,  0.5, γ = 2

For each distribution, plot the survivorship function and the hazardfunction and find:

(a) The mean

(b) The variance

(c) The coefficient of variation

Which distribution gives the larger probability of surviving at least 3 unitsof time?

(iv) Suppose that the survival time follows the lognormal distribution with μ= 1 and σ = 0.5. Find:

(a) The mean survival time

(b) The variance

(c) The coefficient of variation

(d) The median

(e) The mode