Question

A random variable X has the following probability distribution :

X	0	1	2	3	4	5	6	7
P(X)	0	k	2k	2k	3k	k2	2k2	7k2 + k

Determine: 

(i) k 

(ii) P(X < 3) 

(iii) P(X > 4)

Answer 1

(i) Since P (x) is a probability distribution of x,

(ii) P(X< 3) = P(0) + P(1) + P(2)

= 0 + k + 2k 

= 3k

= 3(1/10)

= 3/10

(iii) P(0 < X < 3) = P (1) + P (2) 

= k + 2k 

= 3k

= 3(1/10)

= 3/10