Question

The probability distribution of a discrete r.v.X is as follows.

x	1	2	3	4	5	6
P(X = x)	k	2k	3k	4k	5k	6k

Complete the following activity.

Solution: Since `sum"p"_"i"` = 1

P(X ≥ 3) = `square - square - square  = square`

Answer 1

Since `sum"p"_"i"` = 1

k + 2k + 3k + 5k + 6k = 1

∴ 21k = 1

∴ k = `1/21`

P(X ≥ 3) = 1 – P(X < 3)

= 1 – P(X = 1) – P(X = 2)

= 1 – k – 2k

= `1 - 1/21 - 2/21`

= `6/7`