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Exercise 3: 1. The pH, a measure of the acidity of water, is important in studies...


Exercise 3:
1. The pH, a measure of the acidity of water, is important in studies of acid
rain. For Lake Ontario, baseline measurements on acidity are made so any
changes caused by acid rain can be noted. The pH of water samples from
Lake Ontario is a random variable X with probability density function:
f(x) =
8><
>:
cx, 0 x < 1
c(2 − x), 1 x 2
0, elsewhere
(a) Find the value of c that makes this a probability density function.
(b) Find the cumulative distribution function of X.
(c) What is the probability that X falls between 1/2 and 3/2?.

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