Problem 83E

In Exercise 5.42, we determined that the unconditional probability distribution for Y, the number of defects per yard in a certain fabric, is

Find the expected number of defects per yard.

Reference

The number of defects per yard Y for a certain fabric is known to have a Poisson distribution with parameter λ. However, λ itself is a random variable with probability density function given by

Find the unconditional probability function for Y .

Elements of Statistics – Chapter 5 Notes Probability – The chance an event will occur Sample Space – Includes all possible outcomes in an experiment Event – A subset of the sample space NEVER EXCEEDS THE SAMPLE SPACE EX 1.)Coin is tossed twice. What’s the sample space o HH , HT, TH, TT Probability Rules Always a value between 0 and 1 / (0% - 100%) Probability of an IMPOSSIBLE event is always 0 Probability of an event that must occur is 1 P(event) = # of possible outcomes in an event Total # of outcomes Venn Diagram Complement of NOT A A = NOT A A Complement of Event A – Includes all outcome