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Question
The following is the p.d.f. of continuous r.v.
f (x) = `x/8`, for 0 < x < 4 and = 0 otherwise.
Find expression for c.d.f. of X
Solution
Let F(x) be the c.d.f. of X
Then F(x) =` int_(-∞)^x f (x) dx`
=` int_(0)^-∞f (x) dx + int_(0)^xf (x) dx`
= 0+`int_(0)^x x/8 dx`
=`1/8[x^2/2]_0^x`
= `1/8[x^2/2-0] = x^2/16`
∴ F (x) = `x^2/16`
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