MathML demo
Bernoulli Trials
P
(
E
)
Probability of event E: Get exactly k heads in n coin flips.
=
(
n
k
)
Number of ways to get exactly k heads in n coin flips
p
Probability of getting heads in one flip
k
Number of heads
(
1
-
p
)
Probability of getting tails in one flip
n
-
k
Number of tails
Cauchy-Schwarz Inequality
(
∑
k
=
1
n
a
k
b
k
)
2
≤
(
∑
k
=
1
n
a
k
2
)
(
∑
k
=
1
n
b
k
2
)