Continuous Random Variables

Probability Density Functions(PDF)

From yesterday

Hopefully you noticed:

Also if X and Y are independent random variables

Probabilities of a CRV

The total area under a probability density function is equal to 1

Particular probabilities are found by finding the areas under the curve between the required values.

ExampleA random variable has the pdf:

a) Draw the pdfb) Find P(X<12)c) Find P(X>22.5)d) Find P(6.3<X<11.8)

Example

A bakery producing pastry sheets believes that the thickness of the sheets is uniformly distributed between 1.5mm and 2.0mm. Pastry sheets with a thickness below 1.6mm are rejected. What percentage of the sheets are rejected?

Page 128 – 139 can now all be done…

Tomorrow we will look at the triangle distribution then have Friday in class to work on problems to try catch up.

If you need more questions than your homework book I will have some others…