# The p.d.f. of a continuous r.v. X is f(x) = {3x28for0<x<20otherwise.Determine the c.d.f. of X and hence find P(X < –2) - Mathematics and Statistics

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The p.d.f. of a continuous r.v. X is

f(x) = {((3x^2)/(8), "for" 0 < x < 2),(0, "otherwise".):}
Determine the c.d.f. of X and hence find P(X < –2)

#### Solution

F(x) = int_0^x(x)*dx

= int_0^x (3x^2)/(8)*dx

= (3)/(8) int_0^x x^2*dx

= (1)/(8)[x^3]_0^x

= x^3/(8)

P(X < –2)
= F(–2)
= 0       ...[("f"(x) = 0  "if"  x ∉ (0.2)),(therefore "F"(x) = 1  "for"  x ≤ 0)]

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.2 | Q 1.09 | Page 145