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Econometrics

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Probability Density Function Example

EMETRC-G6XLKV

Suppose that $X$ describes the random variable that can take on only three values, $X = (1,2,3)$. The probability density function is:

$$f(x) = \left\{ \begin{array}{ll} \frac{x^2}{14}, & x \in X \\\ 0, & \text{otherwise} \end{array} \right. $$

Which of the following is TRUE?

A

$Pr[x<3] = \cfrac{5}{14}$

B

$Pr[x>3] = \cfrac{9}{14}$

C

$Pr[x=3] = \cfrac{3}{14}$

D

$Pr[x<2] = \cfrac{5}{14}$

E

$Pr[x>2] = \cfrac{6}{14}$