Question

The probability distribution function of a random variable X is given by

xi :	0	1	2
pi :	3c3	4c − 10c2	5c-1

where c > 0  Find: P (X < 2) 

Answer 1

P (X < 2) 

\[= P\left( X = 0 \right) + P\left( X = 1 \right)\]
\[ = 3 c^3 + 4c - 10 c^2 \]
\[ = \frac{1}{9} + \frac{4}{3} - \frac{10}{9}\]
\[ = \frac{1 + 12 - 10}{9}\]
\[ = \frac{3}{9}\]
\[ = \frac{1}{3}\]