Once an individual has been infected with a certain disease , let X represent the time ( days ) that elapses before the individual becomes infectious. The article "The Probability of Containment for Multitype Branching Process Models for Emerging Epidemics" (J. of Applied Probability, 2011: 173-188) proposes a Weibull distribution with α = 2.2, β= 1.1, and γ= 0.5. Required:
a. Calculate P(1 < X < 2).
b. Calculate P(X > 1.5).
c. What is the 90th percentile of the distribution?
d. What are the mean and standard deviation of X?