1.7. Exercises for Chapter 1
Let X be an r.v. of distribution function
Calculate the probabilities:
Given the random vector Z = (X,Y) of probability density where K is a real constant and where , determine the constant K and the densities fX and fY of the r.v. X and Y.
Let X and Y be two independent random variables of uniform density on the interval [0,1]:
1) Determine the probability density fZ of the r.v. Z = X + Y;
2) Determine the probability density fU of the r.v. U = X Y.
Let X and Y be two independent r.v. of uniform density on the interval [0, 1]. Determine the probability density fU of the r.v. U = X Y.
U takes its values in [0,1]
Let FU be the distribution function of U:
– if u ≤ 0 FU (u) = 0; if u ≥ 1 FU (u) = 1;
where is the cross-hatched area of the figure.
Under consideration ...