Question

Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1),  "for"  x = 1"," 2"," 3"," 4),(2"k"x,  "for"  x = 5"," 6"," 7),(0,  "Otherwise"):}`
where k is a constant. Calculate E(X)

Answer 1

Now the probability distribution is

X	1	2	3	4	5	6	7
P(X)	`2/50`	`3/50`	`4/50`	`5/50`	`10/50`	`12/20`	`14/50`

E(X) = `1 xx 2/50 + 2 xx 3/50 + 3 xx 4/50 + 4 xx 5/50 + 5 xx 10/50 + 6 xx 12/50 + 7 xx 14/50`

= `2/50 + 6/50 + 12/50 + 50/50 + 72/50 + 98/50`

= `260/50`

= `26/5`

= `5.2