Summary: Math 501. 7­th Homework. Due Monday, December 10, 2007.
Homework on "Transformations of random variables".
1. Let X be a r.v. uniformly distributed on (0, 1). Find a function g(x) such that
Y = g(X) has a binomial distribution with parameters n = 3 and p = 1/4.
2. Let X be a random variable with density function
fX(x) =



3x2
2
, -1 < x < 1,
0 elsewhere.
Find the density of Y =

5 - X3.
3. Find the density of the r.v. Y = 1 - X2
, if the density of X is given by
fX(x) =
3

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

Collections: Mathematics