1. X is a continuous random variable with Probability Ddensity
Function given below:

f(x) = 1/(x^2) : x > 1

a) Solve for the mean of X. If you host reservations with your
answer, please discuss what you think your solution is telling you
about X and its mean

b) Solve for the median of X.

c) Solve for the variance and the standard deviation of X. As in
part c., please discuss.

2. Data collected in a city suggested that rainfall duration X
(in hours) can be modeled as a continuous distribution with
Probability Density Function given below:

f(x) = 0.5e^(-0.5x) x > 0

a) Verify that f(x) is indeed a PDF.

b) What proportion of rainfall durations at this location are
between 1 and 2 hours?

c) What must the duration of a rainfall be to place it among the
longest 10% of all time?

d) What is the median of the rainfall duration at this
location?