Lecture Notes Chapter 4 Section 04

Lecture Notes Chapter 4 Section 04 - MATH1780:...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 1780: Introduction to Probability Instructor: Jason Snyder
Background image of page 1

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

View Full DocumentRight Arrow Icon
Contents Continuous Random Variables and Their Probability  Distributions Expected Values of Continuous Random variables The Uniform Distribution The Exponential Distribution The Gamma Distribution The Normal Distribution The Beta Distribution The Weibull Distribution Moment-Generating Functions for Continuous Random  Variables
Background image of page 2
Suppose an experimenter is measuring the life  expectancy X of a transistor. In this case, X can take on an infinite number of  possibilities. We can not assign a positive probability to each  possible outcome of the experiment because, no  matter how small we might make these  probabilities, they would sum to a number greater  than 1 when accumulated.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Let’s consider a specific example to try to  understand what is going on here. Suppose we measure the life expectancy of 50  transistors of a certain type. 0.406 0.685 4.778 1.725 8.223 2.343 1.401 1.507 0.294 2.230 0.538 0.234 4.025 3.323 2.920 5.088 1.458 1.064 0.774 0.761 5.587 0.517 3.246 2.330 1.064 2.563 0.511 2.782 6.426 0.836 0.023 0.225 1.514 3.214 3.810 3.334 2.325 0.333 7.514 0.968 3.491 2.921 1.624 0.334 4.490 1.267 1.702 2.634 1.849 0.186
Background image of page 4
Here is a “histogram” for the data on the previous  slide: An approximate equation for the black line in the  histogram is  2 2 1 ) ( x e x f - =
Background image of page 5

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

View Full DocumentRight Arrow Icon
What if we want to calculate the probability that a  transistor of this type will last for more than 400  hours? Looking at the chart, we notice that probabilities  are indicated by areas under the curve, i.e., an  integral. Thus 
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 29

Lecture Notes Chapter 4 Section 04 - MATH1780:...

This preview shows document pages 1 - 7. Sign up to view the full document.

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