REMEMBER TO DRAW PICTURES!
Basic Distribution Properties
f (x) is a p.d.f./p.m.f. i f (x)dx/ x f (x) = 1
When f (x) is continuous uniform,
1
for a < x < b
ba
f (x) =
0
o.w.
When f (x) is discrete uniform,
0
for x < a
x a
for a x < b
f (x) =
ba
1
for x b
R
The Uniform Distribution of Integers
1
for x = 1,2,.,k
k
p.m.f. of X is f (x) =
0 otherwise
Binomial Pr(X = x) =
n
x
px q nx for x = 0, 1, ., n.
b
f (x)dx cond: (1) f (x) 0 x, (2)
Probability Density Function (pdf ) Pr(a X b) =
f (x)dx = 1
a
1
Uniform Dis
Probability Properties (Take probability of both sides)
A = (A B c ) + (A B ) / Ac B c = (A B )c / Ac B c = (A B )c / (A B ) = A + B AB
Probability in a nite space
n
Pr
n
Ai
n
i=1
n
Pr(Ai )
=
i=1
n
Pr(Ai Aj Ak ) . + (1)n Pr
Pr(Ai Aj ) +
i<j
Ai
i=1
i<j<k