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Verify whether each of the following f...

Verify whether each of the following functions can be regarded as p.mf for the given value of X :
(1)
(2) `P(X) = {{:((x-1)/(3), x = 1","2","3),(0,"Otherwise"):}`

Text Solution

Verified by Experts

p.m.f of random variable should satisfy the following conditions :
(a) `0 lep_(i) le 1` (b)` sump_(i) = 1`
(1) Here `P(X = - 1) = - 0.1 lt 0`
Hence , P(X = x) cannot be regarded as p.m.f of the random variable X.
(2) We have
`P(x) = {{:(,(x-1)/(3),x =1","2","3),(,0, "Otherwise"):}`
This can be written as :

Here, (a) `0 le p_(n) le 1`
(b) `sum p_(i) = 0 +(1)/(3)+(2)/(3) = 1`
Hence, P[X = x] can be regarded as the p.m.f of the random variable X.
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