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The following is the p.d.f. of continuous r.v. f (x) = x8, for 0 < x < 4 and = 0 otherwise. Find expression for c.d.f. of X - Mathematics and Statistics

Sum

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

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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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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Exercise 7.2 | Q 8.1 | Page 239
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