Question

The probability distribution of a random variable X is given below:

X	0	1	2	3
P(X)	k	`"k"/2`	`"k"/4`	`"k"/8`

Determine P(X ≤ 2) and P(X > 2)

Answer 1

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= `"k" + "k"/2 + "k"/4`

= `(7"k")/4`

= `7/4 xx 8/15`

= `14/15`

And P(X > 2) = P(X = 3)

= `"k"/8`

= `1/8 xx 8/15`

= `1/15`