# Suppose error involved in making a certain measurement is a continuous r. v. X with p.d.f. f(x) = {k(4-x2) for-2≤x≤20 otherwise.compute P(X > 0) - Mathematics and Statistics

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Suppose error involved in making a certain measurement is a continuous r. v. X with p.d.f.

f(x) = {("k"(4 - x^2),  "for" -2 ≤ x ≤ 2),(0,  "otherwise".):}
compute P(X > 0)

#### Solution

Given that f(x) represents a p.d.f. of r.v. X.

∴ int_-2^2 f(x)*dx = 1

∴ int_-2^2 "k"(4 - x^2)*dx = 1

∴ "k"[4x - x^3/3]_-2^2 = 1

∴ "k"[(8 - 8/3) - (-8 + 8/3)] = 1

∴ "k"(16/3 + 16/3) = 1

∴ "k"(32/3) = 1

∴ k = (3)/(32)

F(x) = int_-2^2 f(x)*dx

= int_-2^2"k"(4 - x^2)*dx

= (3)/(32)[4x - x^3/3]_-2^2

= (3)/(32)[4x - x^3/3 + 8 - 8/3]

∴ F(x) = (3)/(32)[4x - x^3/3 + 16/3]

P(X > 0) = 1 – P(X ≤ 0)

= 1 – F(0)

= 1 - (3)/(32)(0 - 0 + 16/3)

= 1 - (1)/(2)

= (1)/(2).

Concept: Probability Distribution of a Continuous Random Variable
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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 1.07 | Page 145