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 ≤ 4) = `square + square + square + square = square`

Answer 1

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

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

∴ 21k = 1

∴ k = `1/21`

P(X ≤ 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= k + 2k + 3k + 4k

= `1/21 + 2/21 + 3/21 + 4/21`

= `10/21`