Determine whether the following are valid probability distributions or not. Type "VALID" if it is valid, or type "INVALID" if it is not a valid probability distributions.

(a)

$x$	$1$	$3$	$4$	$8$
$P(x)$	$0.1$	$0.5$	$0.2$	$0.2$

answer:

(b)

$P(x) = \frac{1}{3 x}$, where $x = 1,2,3,...$

answer:

(c)

$x$	$1$	$3$	$4$	$8$
$P(x)$	$0.2$	$0.1$	$-0.2$	$0.9$

answer: