STAT 1430 Lecture Notes - Lecture 14: Random Variable, Gm Family 0 Engine, Weighted Arithmetic Mean

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Thursday, February 21, 2019
STAT1430.01—Lecture14—Random Variables
-The mean of a discrete random variable
A weighted average of the possible outcomes; weights are the probabilities
-Possible outcomes: x1, x2, … xk Call them x
-Probabilities: p1, p2, … pk Call them P(x)
Notation: !
Formula: !
-The mean of a discrete random variable
Average of all possible values in whole population and The overall expected value of x
!
-!=average of sample
-! (constant)= average of population
-Discrete example: Family size (X)
Mean family size is:
-!=1*0+2*0.42+3*0.23+4*0.21+5*0.09+6*0.03+7*0.02=3.14
Interpret this result:
-average family size for the entire population
-Rules of Means #1—Linear Transformations
Linear transformation:
-multiply x by constant and/or add a constant.
Example:
-10% salary raise + $500 bonus
-Y=1.10x + 500
Rule:
μx
μx=xp(x)
¯
XμX
¯
X
μX
Numbers
1
3
4
5
6
Family
Probability
0
0.23
0.21
0.09
0.03
μx=
x
xp(x)
1
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Document Summary

The mean of a discrete random variable: a weighted average of the possible outcomes; weights are the probabilities. Possible outcomes: x1, x2, xk call them x. Probabilities: p1, p2, pk call them p(x: notation: , formula: ! The mean of a discrete random variable: average of all possible values in whole population and the overall expected value of x. Average family size for the entire population. Rules of means #1 linear transformations: linear transformation: Multiply x by constant and/or add a constant: example: A x+b = y = a x + b. Y = 1. 10 x + 500: note: this rule holds for any x, y. Example: cancun temperatures: the mean temperature in cancun is 28. 5 degrees centigrade ( c). What is the mean temperature in fahrenheit (f): f=9/5 c + 32. Example: 0 degrees c = 32 degrees f: mean of f = ! Rule #2 of means sums and differences: rule: 2 random variables x and y.

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