Finding a distribution function

Question

Let $R>0$ and $X\sim Uniform[0,R]$. Let $Y=\min(X, \frac{R}{10})$.Find the distribution function of $Y$.

I can't understand how to solve this. Any help is appreciated.

Answer 1

By definition $F_Y(y)=P(Y\leq y)$. If $0\leq y\leq R/10$, then $F_Y(y)=F_X(y)=y/R$; if $y>R/10$, then $F_Y(y)=1$; if $y<0$, $F_Y(y)=0$