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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) = ______
Options
`343/297`
`294/251`
`297/294`
`294/297`
Solution
`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) = Σxi Pi
= 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`
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