# It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by f (x) otherwise (i) Verify whether f (x) is p.d.f. of r.v. X. - Mathematics and Statistics

Sum

It is known that error in measurement of reaction temperature (in 0° c) in a certain experiment is continuous r.v. given by

f (x) = x^2 /3 , for –1 < x < 2 and = 0 otherwise

Verify whether f (x) is p.d.f. of r.v. X.

#### Solution

f (x) = x^2/3 ≥0, for -1 < x < 2

Also,  int_(-∞)^∞ f (x) dx

=int_(-∞)^-1 f (x) dx+ int_(-1)^2 f (x) dx  +int_(2)^∞f (x) dx

= 0+int_(-1)^2 f (x^2/3) dx + 0 = 1/3[x^3/3]_-1^2

= 1/3[8/3 - ((-1))/3] = 1/3[9/3] = 1

∴ f (x) is the p.d.f. of X.

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 7 Probability Distributions
Exercise 7.2 | Q 3.1 | Page 239