Moderate# Discrete Probabilities with PMF

STATS-NE0EZO

Suppose $X$ is a random variable whose probability mass function $p(x)$ is given by:

$$ p(x)=\begin{cases} .1 &\mbox{if } x=.15, .25\\\ .25 &\mbox{if } x=.05, .2\\\ .3 &\mbox{if } x=.35 \end{cases} $$

How many of the following statements are **TRUE**?

i.$P(X=.3)=.35$

ii.$P(X=0)$ cannot be determined

iii.$P(X<.2)=.35$

iv.$P(Y<0)=.3$ where $Y=X-.3$

v.$P(X>Y)=1$ where $Y=X-.3$