Let X have a continuous uniform distribution on the interval (1; 2). In other words, the pdf of X is f(x) = 1/3; for 1 < x < 2 (and it is zero otherwise). Moreover, De?ne the following random variables: Y = 2X + 1; W = X^2 and Z = piecewise function of it being 0 when X is less than and equal to 0 and 1 for X greater than 0.
(a) Obtain the cdf of X. Then compute P(0 < X < 1).
(b) Obtain the cdf of Y . Then determine the pdf of Y .
(c) Obtain the cdf of W. Then determine the pdf of W.
(d) Determine the pmf and cdf of Z.