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:  c 

Answer 1

We know that the sum of probabilities in a probability distribution is always 1.
∴ P (X = 0) + P (X = 1) + P (X = 2) = 1

\[\Rightarrow 3 c^3 + 4c - 10 c^2 + 5c - 1 = 1\]
\[ \Rightarrow 3 c^3 - 10 c^2 + 9c - 2 = 0\]
\[ \Rightarrow \left( c - 1 \right)\left( 3 c^2 - 7c + 2 \right) = 0\]
\[ \Rightarrow \left( c - 1 \right)\left( 3c - 1 \right)\left( c - 2 \right) = 0\]
\[ \Rightarrow c = \frac{1}{3}, 1, 2\]
\[\left( \text{ Neglecting 1 and 2 as individual probability should not be greater than one} \right)\]