These notes assume you have basic knowledge of the Binomial Distribution. They're still pretty explanatory.

## TI - The Binomial Distribution

If X ~ B (n, p)

Where X is a discrete variable

n is the number of trials

p is the probability of success

E(X) = np

Var(X) = npq

Where q = 1 – p

With the TI, you can calculate the probabilities of X being equal to, less than (or equal to), more than (or equal to) and being in between two values.

e.g. when X ~ B (10, 0.1)

i) Find P(X=5)

Open up a calculator document, and click menu:

Where X is a discrete variable

n is the number of trials

p is the probability of success

E(X) = np

Var(X) = npq

Where q = 1 – p

With the TI, you can calculate the probabilities of X being equal to, less than (or equal to), more than (or equal to) and being in between two values.

e.g. when X ~ B (10, 0.1)

i) Find P(X=5)

Open up a calculator document, and click menu:

P(X=5) = 0.001488…

= 0.0015 (4.d.p.)

ii) Find P(X≤3) (this is the same as P(X<4)) This time, you’re going to use the Cumulative Distribution Function (cdf):

(It’s right under the pdf we used last example)

= 0.0015 (4.d.p.)

ii) Find P(X≤3) (this is the same as P(X<4)) This time, you’re going to use the Cumulative Distribution Function (cdf):

(It’s right under the pdf we used last example)

P(X≤3) = 0.987205…

= 0.9872 (4.d.p.)

iii) Find P(X>4) (this is the same as P(X≥5)

= 0.9872 (4.d.p.)

iii) Find P(X>4) (this is the same as P(X≥5)

Doesn’t include 2, but includes numbers higher than 2 and less than and including 6

P(2<X≤6) = 0.070182…

= 0.0702 (4.d.p.)

= 0.0702 (4.d.p.)