Page 43 - Math SL HB Sem 3

Probabi I ity Distributions
- probabilities of each result obtained in an experiment

Terms to know:
1) Random variable, X - a measurable quantity whose value is the result obtained in an experiment, x

. Discrete random variable . Continuous random variable
- the data only takes certain - the data can take any numerical
discrete numerical values values in a given range
E-9. number on a die E.g. height, length, weight,
numberof cards selected... etc. temperature, speed ... etc.

2) Probability Distribution - the probability associated with each measured value of an experiment.
- can be represented as a table or graph, or given as a function.

A fair die has faces marked with number 1, 3, 3, 3, 4, 4.

)The random variable, X, is the number shown on the die when it is thrown
)The results obtained, .x, can be 1, 3, 4.
tThe probability distribution for x is:

x i 3 4
7 31 27
P(X : x)
a 62 63

It 7,ust satisfi/:
I 1

3) Expectation, f,(X) the mean/expected value of the random variable X
-

E,;x):lxf g: x1)
i

\. Exampl
For the above example,

111
E(x) = 1xa+3xr+4x5 = 3

I