Statistics and Probability

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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 $Y=X-.3$

A

$0$

B

$1$

C

$2$

D

$3$

E

$4$

F

$5$