Question

If the p.m.f. of a d.r.v. X is P(X = x) = `{{:(("c")/x^3",", "for"  x = 1","  2","  3","),(0",", "otherwise"):}` then E(X) = ______

विकल्प

• `343/297`

• `294/251`

• `297/294`

• `294/297`

Answer 1

`bb(294/251)`

Explanation:

P(x = 1) + P (x = 2) + P (x = 3) = 1

`"C"/1+"C"/8+"C"/27` = 1

`(216"C"+27"C"+8"C")/216` = 1

E (X) = Σx_i P_i

= 1 × P (x = 1) + 2 × P (x = 2) + 3 × P (x = 3)

= `1xx"C"/1+2xx"C"/8+3xx"C"/27`

= `"C"/1+"C"/4+"C"/9`

= `(36"C"+9"C"+4"C")/36`

= `(49"C")/36`

= `49/36xx216/251`

= `(49xx6)/251`

= `294/251`