Flashcards in Chapter 6 Random Variables Deck (11):

1

## random variable

### takes numerical values that describe the outcomes of some chance process

2

## probability distribution

### gives its possible values and their probabilities

3

## the standard deviation of x

### the square root of the variance

4

## continuous random variable X

### takes all values in an interval of numbers, it is described by a density curve, the probability of any event is the area under the density curve and above the values of X that make up the event

5

## independent random variables

### if knowing the event of one variable has occurred tells us nothing about the occurrence of another variable occurring

6

## binary setting

###
preforming several independent trials of the same chance process and record the number of TIMES that particular outcome occurs.

Binary? possible outcomes of each trial, classified as "success" or "failure"

Independent? trials must be independent; knowing the result of one trial must not effect the result of any other trial

Number? number of trials n of the chance process must be fixed in advance

Success? on each trial, the probability p of success must be the same

7

## binomial random variable

### the count X of successes in a binomial setting

8

## binomial distribution

### the probability distribution of X, with parameters n and p, where n is the number of trials of the chance process and p is the probability of a success on any one trial. possible values of X are the whole numbers from 0 to n

9

## geometric setting

###
preforming independent trials of the same chance process and record the number of TRIALS until that particular outcome occurs

Binary? possible outcomes of each trial can be classified as "success" or "failure"

Independent? trials must be independent: knowing the result of one trial must not have any effect on the result of any other trial

Trials? the goal is to count the number of trials until the first success occurs

Success? on each trial, the probability p of success must be the same

10

## geometric random variable

### the number of trials Y that it takes to get a success in a geometric setting

11