Summary: Exercises Introduction to Stochastic Processes, week 1
Exercises 10-13 are particularly representative of exam exercises.
Let X be a non-negative random variable with E[X2
] < , having probability
density function f(·). The following formula was derived during the lectures:
P(X > u)du.
2uP(X > u)du.
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?