Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

Challenge questions

1.

Let $X$ have a continuous distribution with pdf $f_{X}$ , for $f_{X}(x)>0$ for $-\infty<x<\infty$ . Let $Y=aX+b$ where $a>0$ . Find the pdf of $Y$ , expressed in terms of the pdf $f_{X}$ .
2.

Let $X$ have cdf $F_{X}$ , and assume $F_{X}$ is continuous and strictly increasing. Let $Y=F_{X}(X)$ . Find $P(Y\leq y)$ for $0<y<1$ . What is the distribution of $Y$ ?