Solutions - 5100-01

(1) Find the possible values of $Y$:

After the decimal point, any of the 10 digits can appear, so $Y\in \{0,1,\dots ,9\}$.

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(2) Find the PMF of $Y$:

Each digit has a $\frac{1}{10}$ chance of appearing.

$$P_Y(y)=\{\begin{array}{cc}\frac{1}{10}& y\in \{0,1,\dots ,9\}\\ 0& \text{otherwise}\end{array}$$

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(3) Find the CDF of $Y$:

$$F_Y(y)=\{\begin{array}{cc}0& y<0\\ \frac{1}{10}(y+1)& 0\le y\le 9\\ 1& 9<y\end{array}$$