1. Clicker Question 1 What, in radical form, is the Simpson’s Rule estimate (with n = 2) of the surface area generated by rotating y =  x about the x- axis between x = 0 and x = 2? – A.  (1 +  3 +  5 +  7 +  9) – B.  (1 + 4  3 + 2  5 + 4  7 +  9) – C.  /3 (1 + 4  3 + 2  5 + 4  7 +  9) – D.  /6 (1 + 4  3 + 2  5 + 4  7 +  9) – E.  /6 (1 + 2  3 + 4  5 + 2  7 +  9)

2. Probability (10/7/13) A continuous random variable X represents all the values some physical quantity can take (e.g., heights of adult males, lifetime of a type of light bulb, etc., etc.) A probability density function f for X is a function whose integral from a to b gives the probability that X lies between a and b. A density function must be non-negative and must satisfy that its improper integral from -  to  is 1.

3. Example Show that f (x) = 0.006x(10 – x) on [0, 10] and 0 elsewhere is a density function. If X is a random variable whose density function is f, what is the probability X has a value between 1 and 5?

4. Clicker Question 2 Using the density function on the previous slide, what is the probability that X is greater than 3? – A. 0.667 – B. 0.784 – C. 0.284 – D. 0.845 – E. 0.392

5. Mean Value of a Random Variable We can compute the mean, or average, value of a random variable by adding up each of its values weighted by the probability of that value, i.e. compute In our example, what is the mean value of the variable (obvious from the symmetry of f, but work it out)? Question: What, in general, would the median be?

6. The Normal Density Function The “mother of all density functions” is the normal density function where  is the mean and  is the standard deviation. Note that we cannot use the Fundamental Theorem to calculate probabilities with the function. Hence we must use numerical methods instead.

7. Assignment for Wednesday Read Section 8.5. In that section, please do Exercises 1, 4, 5, and 9. Wednesday’s class will have no clicker questions. We will go over this last material and then review as needed. Test #1 is on Friday. You can start at 8:30 if you wish. One reference sheet can be used.