All these questions are answered using the basic definitions and formulae. What have you tried and where do you get stuck?
Note: How to do 1. is given here: http://www.mathhelpforum.com/math-he...-homework.html
The p.d.f of X is f(x) = {x if 0 ≤ x ≤ 1} and {c/x^3 if 1 ≤ x < 1} and 0 elsewhere. Find:
1. the value of c such that f(x) is a p.d.f.
2. the mean of X, if it exists.
3. the variance of X , if it exists.
4. P(1/3 < X ≤ 3).
All these questions are answered using the basic definitions and formulae. What have you tried and where do you get stuck?
Note: How to do 1. is given here: http://www.mathhelpforum.com/math-he...-homework.html