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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:
Picture
Picture
​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)
Picture
P(X≤3) = 0.987205…
 
= 0.9872 (4.d.p.)

​iii) Find P(X>4) (this is the same as P(X≥5)
Picture
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.
Picture
​Doesn’t include 2, but includes numbers higher than 2 and less than and including 6
Picture
​  P(2<X≤6) = 0.070182…
 
 = 0.0702 (4.d.p.)
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