Random Variables Flashcards
1
Q
Necessary conditions for a probability function?
A
- p(x) is not negative
-sum of all p(x) = 1
2
Q
How to work out E(x) for a DRV?
A
sum of x p(x)
3
Q
Can you take out non linear from E(x)?
A
-no only linear
4
Q
Var (x) ?
A
E(x)^2 - (E(x))^2
5
Q
Var (ax+b)
if a and b are constants?
A
-a^2 Var (x)
6
Q
sd(ax+b)?
A
l a l sd(x)
7
Q
Expectation of a constant?
A
- just the constant
8
Q
Variance and SD of constant?
A
0
9
Q
MGF of a DRV?
A
E(e^tx) = Mx(t)
10
Q
E(x) from MGF?
A
M’x(0)
11
Q
E(x^2) from MGF?
A
M’‘x(0)
12
Q
Same MGF?
A
-same distribution
13
Q
f(x) for CRV?
A
-f(x) is not a probability, area under curve
14
Q
Properties of PDF?
A
-f(x) is positive and 0
- limits infinity to negative infinity f(x) = 1
15
Q
How to get CDF?
A
-integrate f(x) with lowest possible value
16
Q
E(x) for CRV?
A
same thing as DRV but integral instead of summation
17
Q
median of a CRV?
A
F(m) = 0.5
