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Suppose a discrete random variable can o...

Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by
`f(x)={{:((x^(2)+1)/k",", "for x=0,1,2"), (0, "otherwise"):}`
Find (i) the value of k (ii) cumculative distribution function (iii) `P(X ge 1)`.

Text Solution

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The correct Answer is:
(i) k=1
(ii) cumculative distribution function is
`f(x)={{:(1/8, "for", x le 0), (2/8+1/8, =, 3/8"for "x le 1), (3/8+5/8=1, "for", x le 2):}`
(iii) `7/8`
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