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Suppose $f(x)$ is the probability density function of some continuous random variable $X$.

How many of the following statements MAY be true?

i. $f(x)=5$ for $x=0$.

ii. $f(10)=P(X=10)$.

iii. $f(10)\neq P(X=10)$.

iv. The area under the curve $f(x)$ between 1 and 2 is equal to 2.

v. The area under the curve $f(x)$ between 1 and 2 is equal to 0.

vi. $P(X=f(5))=.3$

A

$1$

B

$2$

C

$3$

D

$4$

E

$5$

F

6

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