Cultural Cocktail

SLIDE 11: explain the formula Binomial dist.

This is a probability tree for 3 trials.

To calculate the probability that there are x successes in n trials,

For each success in the sequence we must multiply by p.

And if there are c successes, there must be (n-x) failures. For each failure we multiply by (1-P).

Thus, the probability for each sequence of branches that produce x successes and n-x failures, is p^x гЂ-(1-p)гЂ--^(n-x)

There are a number of branches that yield x successes and (n-x) failures. To count the number of these branch sequences we use combinatorial formula

_n C_x n!/x!(n-x)!

Read page 217 Binomial random variable section.

SLIDE 30 : POISSON versus BINOMIAL random variables.

Like the binomial the Poisson random variable is the number of occurrences of events (which we will continue to call successes).

The difference between the two random variables is that

A binomial random variable is the number of successes in a set of trials, whereas

A Poisson random variable is the number of successes in an interval of time or specific region of space.

Examples of Poisson random variables:

The number of cars arriving at a service station in 1 hour (the interval of time is 1 hour.)

The number of flaws in a bolt of a cloth. (the specific region is a bolt of a cloth.)

The number of accidents in 1 day on a particular stretch of highway. (the interval is defined by both time, 1 day, and space, the particular stretch of highway.)

SLIDE 22 : EXAMPLE OF BINOMIAL RANDOM VARIABLE and DISTRIBUTION (Defining the cumulative probability)

A Student taking statistics course, which

does not read the textbook before class

does not do homework

and regularly misses class.

He intends to rely on luck to pass the next exam.

The exam:

10 multiple-choice questions.

Each question have five possible answers, only one of which is correct

We would