Description

5. Show that
Pr(X > a) = Pr(e−sX > e−sa), s < 0
6. Using (2.2.1), show that (2.5.1)
Pr(X > a) ≤ easMX(s), s < 0 (2.6.1)
1 Definitions
1. The mean of Y is defined as
E(Y) = ∑kpY(k)
k
2. The MGF of X is defined as
∼ N MX(s) = E(e−sX)
3. Let X (0,1). Then the Q function is defined as, Q(x) = Pr(X > x), x ≥ 0
2 Problems
1. Show that
∞
E(Y)∑pY(k), m > 0
k=m
2. Show that
E(Y) (1.1.1)
(1.2.1)
(1.3.1)
(2.1.1)
Pr(Y > m) , m > 0 (2.2.1)
m
3. Using (2.2.1), show that Show that
Pr([Y − E(Y)] > b ) ≤ b2 , 2 2 var(Y)
4. Show that b > 0 (2.3.1)
Pr(|Y , b > 0 (2.4.1)
2
7. Show that the MGF of X is
MX(s) = e12s2
8. Using (2.6.1) show that (2.7.1)
Q (2.8.1)