Summary: Exercises Introduction to Stochastic Processes, week 1
Exercises 10-13 are particularly representative of exam exercises.
Exercise 1
Let X be a non-negative random variable with E[X2
] < , having probability
density function f(·). The following formula was derived during the lectures:
E[X] =

0
P(X > u)du.
Show that
E[X2
] =

0
2uP(X > u)du.
Exercise 2
Let Xi be exponentially distributed with parameter i, i = 1, 2.
(a) Compute P(X1 > u + v | X1 > u).
(b) What is the probability that X1 X2?

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente
Litvak, Nelly - Department of Applied Mathematics, Universiteit Twente

Collections: Engineering