Division of Mathematical Statistics, Lund University
Probability Theory: Problem set 6
Instructor: Dragi Anevsk
TA: Debleena Thacker
Here we mostly provide answers to numerical exercises.
1. E 6.1
Answer:
(a) E[X1 ] = E[X2 ] = 0
(b) Cov(X1 , X2 ) = 0.
2. E 6.2.
Answer:
(a) E[X1 ] = 21 , and V ar(X1 ) =
1
.
22
(b) E[X2 ] = +∞.
(c) Cov(X1 , X2 ) = 0.
3. E 6.3
Answer:
3/2, if we consider the correction of x/2 to x as discussed in the exercise
session.
4. E 6.4
1
Answer:
Y ∼ Exp(2).
5. E 6.5
Answer:
Y ∼ Geom(p̂), where p̂ = 1 − (1 − p)2
2