Discrete
Distribution
Binomial
PMF
Mean Variance When to Use
np
Np(1-p)
! n $ x
Binomial: f (x) = #
& p (1− p)n−x
" x %
Geometric
Geometric: f (x) = p1 (1− p) x−1
1/p
(1-p)/p2
Negative
Binomial
" x −1 % r
f (x) = $
' p (1− p) x−r
# r −1 &
r/p
(1-p)r/p2
x = r, r +1, r + 2...
Example
Problem
Fixed number Probability
of trials n ,
of a radio
Random
station
number of
picking up
successes, x
your call.
You make
10 calls,
what is the
probability
that your
call is
picked up 5
times.
Random
What is the
number of
prob. That
trials x, Fixed
you have
number of
to make 5
success =1,
calls when
until the FIRST they finally
success
pick up on
the 5th call
Number of
What is the
trials until the prob. That
rth success
your
second
answer
called will
be on the
& ()*+, -./+.-.11)23
Normal
P(X≤ 𝑥) Cont. Correction: +0.5. 𝑧 =
4
Approximation
P(X≥ 𝑥) Cont. Correction -0.5
to the
P(X<x) Cont. Correction -0.5
Binomial
P(X>x) Cont. Correction +0.5
np
Np(1-p)
5th
attempt?
When
The
approximating probability
a Binomial
of success
dist. with
is .4. What
large amount is the
of successes
probability
in a large
that there
amount of
will be 600
trials
or more
successes
within
1000 trials.