Question

The p.m.f. of a r.v. X is
P(x) = `{:(= 1/13","  "for"  x = 1","  2","  ......","  14","  13),(= 0","  "otherwise."):}`
Then, E(X) is equal to ______.

Options

• 2

• 4

• 6

• 7

Answer 1

The p.m.f. of a r.v. X is
P(x) = `{:(= 1/13","  "for"  x = 1","  2","  ......","  14","  13),(= 0","  "otherwise."):}`
Then, E(X) is equal to 7.

Explanation:

E(X) = `sumx_"i"*"P"(x_"i")`

= `1(1/13) + 2(1/13) + .... +  12(1/13) + 13(1/13)`

= `1/13 (1 + 2 + 3 + ... + 12 + 13)`

= `1/13 ((13 xx 14)/2)`  ......`[because sum_("r" = 1)^"n" "r" = ("n"("n" + 1))/2]`

= 7