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Continuous random variable

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probability density function -

f(x) = { x^2/ 9 , 0<x<3 (x is greater than or EQUAL to 0 and less than or EQUAL to 3)
{ 0, otherwise

Let Y= 9X/5 + 32. Find E(Y) and STD(Y).

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Solution Summary

Using density function of a variable (x), we estimate expected value and standard deviation of for another variable (y) which is related to variable of given density function.

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probability distribution function (pdf) for x:
f(x) = x^2/9 (for 0 le x le 3); else 0 (NOTE: le: less than or equal to)

Required quantities:

P(X) = integration(0 to 3) (f(x)) dx = integration(0 to 3) (x^2/9) dx = 1

E(X) = integration[0 to 3] (x*f(x)* dx) = integration[0 to 3] (x^3/9) = x^4/(4*9)|[0 to 3] ...

Solution provided by:
Amrit Lal Ahuja, PhD (IP)
Education
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
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