In: Civil Engineering
The groundwater concentration of a chemical in a region (X) is a random variable with probability density function ?? (?) = { 1.2(? + ? 2 ) 0 < ? < 1 0 ??ℎ??????
a) Find the cumulative distribution of X.
b) Graphically illustrate the PDF and CDF if
c) Find the probability that X exceeds 0.5.
d) Find the mean, median and mode of X.
e) Find the standard deviation ? and coefficient of variation of X.
f) Find the probability that the concentration is within ±2? of the mean.
g) Determine the quantile estimation function and Graphically illustrate the function.
h) Find the 90%, 95%, and 99% quantiles of X.