prob.part27.55_56 - 2.1 SIMULATION OF CONTINUOUS...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
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 47 0.5 1 1.5 2 0.2 0.4 0.6 0.8 1 Figure 2.7: Sum of two random numbers. [ a,b ] approximates the probability that a ≤ X ≤ b . But the sum of the areas of these bars also approximates the integral b a f ( x ) dx . This suggests that for an experiment with a continuum of possible outcomes, if we find a function with the above property, then we will be able to use it to calculate probabilities. In the next section, we will show how to determine the function f ( x ). Example 2.5 Suppose that we choose 100 random numbers in [0 , 1], and let X represent their sum. How is X distributed? We have carried out this experiment 10000 times; the results are shown in Figure 2.8. It is not so clear what function fits the bars in this case. It turns out that the type of function which does the job is called a normal density function. This type of function is sometimes referred to as a “bell-shaped” curve. It is among the most important functions in the subjectas a “bell-shaped” curve....
View Full Document

This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.

Page1 / 2

prob.part27.55_56 - 2.1 SIMULATION OF CONTINUOUS...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online