Question

A discrete random variable X has the probability distribution given as below:

X	0.5	1	1.5	2
P(X)	k	k2	2k2	k

Determine the mean of the distribution.

Answer 1

For a probability distribution, we know that if P_i ≥ 0

Mean of the distribution

E(X) = `sum_("i" = 1)^"n" "X"_"i""P"_"i"`

= 0.5k + 1.k² + 1.5(2k²) + 2k

= `"k"/2 + "k"^2 + 3"k"^2 + 2"k"`

= `4"k"^2 + 5/2"k"`

= `4(1/3)^2 + 5/2(1/3)`

= `4/9 + 5/6`

= `23/18`