121616949-math.226

# 121616949-math.226 - P n = Z 13 2 7 2 f x dx Of course we...

This preview shows page 1. Sign up to view the full content.

212 Chapter 9 Applications of Integration EXAMPLE 9.23 Consider again the two dice example; we can view it in a way more that resembles the probability density function approach. Consider a random variable X that takes on any real value with probabilities given by the probability density function in figure 9.16 . The function f consists of just the top edges of the rectangles, with vertical sides drawn for clarity; the function is zero below 1 . 5 and above 12 . 5. The area of each rectangle is the probability of rolling the sum in the middle of the bottom of the rectangle, or P ( n ) = Z n +1 / 2 n - 1 / 2 f ( x ) dx. The probability of rolling a 4, 5, or 6 is
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: P ( n ) = Z 13 / 2 7 / 2 f ( x ) dx. Of course, we could also compute probabilities that don’t make sense in the context of the dice, such as the probability that X is between 4 and 5 . 8. 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 Figure 9.16 A probability density function for two dice. As this example illustrates, we do not require that f be continuous, but we will assume that f has only ﬁnitely many discontinuities (possibly zero), and that the discontinuities are either jump discontinuities or removable (a “hole” in the function). This guarantees...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern