Category Archives: Continuous uniforms

Let \(\Omega = \{(x,y):0 \leq x,0 \leq y \leq \exp(-x/2)\}\).

(a) What is the area of \(\Omega\)?

(b) Suppose \(U = (U_1,U_2)\) is drawn uniformly from \(\Omega\).  Find \(\mathbf{P}(U_1 \leq 2.3)\).

(c) Find \(\mathbf{P}(U_2 \geq 1)\).

(d) For \(a\) an arbitrary positive real number, find \(\mathbf{P}(U_1 \leq a)\).

[Author Mark Huber. Licensed under Creative Commons.]