prob.part25.51_52

# prob.part25.51_52 - 2.1 SIMULATION OF CONTINUOUS...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2.1. SIMULATION OF CONTINUOUS PROBABILITIES 43 1 x 1 y y = x 2 E Figure 2.2: Area under y = x 2 . for this simple region we can find the exact area by calculus. In fact, Area of E = 1 x 2 dx = 1 3 . We have remarked in Chapter 1 that, when we simulate an experiment of this type n times to estimate a probability, we can expect the answer to be in error by at most 1 / √ n at least 95 percent of the time. For 10,000 experiments we can expect an accuracy of 0.01, and our simulation did achieve this accuracy. This same argument works for any region E of the unit square. For example, suppose E is the circle with center (1 / 2 , 1 / 2) and radius 1/2. Then the probability that our random point ( x, y ) lies inside the circle is equal to the area of the circle, that is, P ( E ) = π 1 2 2 = π 4 . If we did not know the value of π , we could estimate the value by performing this experiment a large number of times!...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

prob.part25.51_52 - 2.1 SIMULATION OF CONTINUOUS...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online