Continuous Random Variables - Introductory Probability - 400 Level Class

The speed of a molecule in a uniform gas at equilibrium is a random variable who probability density function is given by f(x) = { ax²e^(-bx²) x≥0 { 0 x<0 where b=m/2kT and k, T and m denote, respectively, Boltzmann's constant, the absolute temperature, and the mass of the molecule. Evaluate a in terms of b.

The problems are from probability class.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. If there is anything unclear in the problem, please tell me. Thank you very much.

The problems are from probability class.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. If there is anything unclear in the problem, please tell me. Thank you very much.

The problems are from probability class.

The problems are from 400 level probability class but introductory course. Please specify the terms you use (if necessary) and explain each step of your solutions. If there is anything unclear in the problem, please tell me. Thank you very much.

Probability Class - Introductory 400 Level - Jointly Distributed Random Variables

2. The joint pdf of X and Y is given by f(x,y)= c(y² - x²)x^(-y), -y ≤ x ≤ y, y>0. a) What is the marginal density of Y? b) What is the value of c? c) What is E(Y)?