Question

3. Twenty-five patients receive treatment for an illness, for which the treatment is supposed to be 87% effective in curing the condition permanently. Assume the patients are independent of each other. Let X = the number of patients who are cured.

(a) What type of random variable is X?    Give the name of the distribution as well as the value of any model parameters.

Answer 1

3. Given twenty-five patients receive treatment for an illness, for which the treatment is supposed to be 87% effective in curing the condition permanently.

i.e. n = 25 and p = 87% = 0.87

Let X = the number of patients who are cured.

Therefore, X follows Binomial distribution with parameters n = 25 and p = 0.87

i.e. X ~ Binom(n=25,p = 0.87)

since i) Patients are independent of each other

ii) Patients are finite and small i.e. less than 30

iii) Each Patient has two outcomes i.e. effective and not effective