HIV Patients. The probability is 0.182 that a person with HIV positive at the age of 20 years will live till 63 years of age. Among 6 HIV positive patients of 20 years, what is the probability that the number of patients alive till 63 years is

a. exactly three?

b. exactly five?

c. at least five?

d. between three and five, inclusive?

e. Determine the probability distribution of the random variable X, the number of patients alive till the age of 63 years.

f. Identify the probability distribution of X as right skewed, symmetric, or left skewed without consulting its probability distribution or drawing its probability histogram.

g. Draw a probability histogram for X.

h. Use your answer from part

(e) and Definitions 5.4 and 5.5 on pages 254 and 256, respectively, to obtain the mean and standard deviation of the random variable X.

i. Use Formula 5.2 on page 267 to obtain the mean and standard deviation of the random variable X.

j. Interpret your answer for the mean in words.