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Statistics and Probability

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Moderate

Identifying Probability Density Functions

STATS-FJE1EB

How many of the following functions can be probability density functions of some continuous random variable $X$?

i. $f(x)=2$ for $0< x< 1/2$

ii. $f(y)=2y$ for $0< y< 1$

iii. $f(x)=\begin{cases} .1 &\mbox{if } x=2, 4\\\ .25 &\mbox{if } x=1, 3\\\ .3 &\mbox{if } x=5 \end{cases}$

iv. $f(x)=x$ for $-1< x< 1$

v. $\rho(x)$ where $\rho(x)$ can be graphed as:

vi. $f(x)$ can be graphed as:

A

$1$

B

$2$

C

$3$

D

$4$

E

$5$

F

$6$