Question

Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf)...

Suppose a random variable X has cumulative distribution function (cdf) F and probability

density function (pdf) f. Consider the random variable Y = X?b

a for a > 0 and real b.

(a) Let G(x) = P(Y x) denote the cdf of Y . What is the relationship between the functions

G and F? Explain your answer clearly.

(b) Let g(x) denote the pdf of Y . How are the two functions f and g related?

Note: Here, Y is called the translated and scaled version of X.

Math   Statistics-And-Probability   
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