# 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

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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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#### 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