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)
P(X>4) = 0.001635…
= 0.0016 (4.d.p) iv) Find P(2<X≤6) |
Choose a suitable upper bound… 10000 is usually your best bet (don’t choose too high or your TI will crash) – as long as it’s safely above your number of trials you will be fine.
|
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.)
