# STAT 1430 Lecture Notes - Lecture 17: Probability Distribution, Random Variable, Standard Deviation

STAT1430.01—Lecture17—Random Variable March 6, 2019

• The mean of a Continuous Random Variable

o Notation:

o Formula:

• Waiting for a cab

o Suppose X=time waiting for a cab, where you will only wait up to 10 minutes.

o Suppose f(x)=3/1000 * 2 where [0<X<10]

o Find the mean waiting time. Include units.

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• Notes on Means

o Always integrate over entire interval for X

o Don’t forget to put the “x” in your integral. What would the result be if you forgot

the x?

o Your answer is not a probability. It’s the expected average value of X.

o Your answer should be somewhere between the minimum and maximum

possible values of x.

o The mean of X is in units of X.

o We expect you to be able to set up and calculate the mean for both discrete and

continuous random variables.

• The Variance of a Continuous Random Variable

o Notation:

o Formula:

• Waiting for a cab

o Suppose X = time waiting for a cab, where you will only wait up to 10 minutes.

o Suppose f(x) = 3/1000 x2 where [0 < X < 10]

o SET UP the variance of the waiting times. Include all details, such as the value of

the mean.

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• Note on Variances

o When finding variances for continuous RV, you only have to SET UP the

integrals, not calculate them out. (See examples for details)