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Transcript
Advice for Chapter 7

Be able to distinguish between a discrete random variable and a continuous random
variable

Understand how to find the expected value of a discrete random variable.
o Expected value is the mean of the probability distribution.
o X  x i p (x i )

o Can also be represented as E(X)
o Does not have to be a whole number
Understand how to find the variance of a discrete random variable
o  2  Var (X )   (x   )2 P (x )

Understand how to find the standard deviation of a discrete random variable.

o   Var (X )
The probability distribution for a continuous random variable is defined in terms of a density
curve. (Think Normal distributions).

You must be able to work with transformations and combinations of random variables.
o These rules apply to any random variables X and Y:
 a bX  a  b X
 2a bX  b 2 2 X
X Y  X  Y
o For independent random variables X and Y:
  2 X Y   2 X   2Y



More Advice
o Do not assume normality. Make sure that normality is justified.
o Watch out for variables that aren’t independent. You will not be able to add their
variances.
o Variances of independent variables add. Standard deviations DO NOT.
o Variances of independent variables add, even when you are looking for the difference.
o Do not write independent instances of a random variable with notation that looks like they
are the same variable. Write X 1  X 2  X 3 instead of X  X  X .

Calculator Functions
o normalcdf (lowerbound, upperbound, mean, std dev)
 gives the probability a.k.a. area under the density curve
 If looking for area to the left of the curve, lowerbound = -1E99
 If looking for area to the right of the curve, upperbound = 1E99
o Invnorm(area, mean, std dev)
 Returns x-values for given area
 Measures from the left of the curve
 Be sure you are reporting the correct area—always draw a picture