Maharashtra State BoardHSC Arts 12th Board Exam
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Verify which of the following is p.d.f. of r.v. X: f(x) = x, for 0 ≤ x ≤ 1 and -2 -x for 1 < x < 2 - Mathematics and Statistics

Sum

Verify which of the following is p.d.f. of r.v. X:

f(x) = x, for 0 ≤ x ≤ 1 and -2 -x for 1 < x < 2

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Solution

f (x) is the p.d.f. of r.v. X if

(a) f (x) ≥ 0 for all x ∈ R and

(b) `int_(- ∞)^∞ f(x) dx = 1`

 f (x) = x ≥ 0 if 0 ≤ x ≤ 1

For 1 < x < 2, < -2 < - x < -1

∴ - 2 - 2 < - 2 - x < - 2 - 1

i.e. - 4 < f(x) <  - 3 if 1< x < 2

Hence, f (x) is not p.d.f. of X.

  Is there an error in this question or solution?
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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 1.2 | Page 238
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