Chapter 6 Random Variables

Question 1

random variable

Answer 1

takes numerical values that describe the outcomes of some chance process

Question 2

probability distribution

Answer 2

gives its possible values and their probabilities

Question 3

the standard deviation of x

Answer 3

the square root of the variance

Question 4

continuous random variable X

Answer 4

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

Question 5

independent random variables

Answer 5

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

Question 6

binary setting

Answer 6

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

Question 7

binomial random variable

Answer 7

the count X of successes in a binomial setting

Question 8

binomial distribution

Answer 8

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

Question 9

geometric setting

Answer 9

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

Question 10

geometric random variable

Answer 10

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

Question 11

geometric distribution

Answer 11

the probability distribution of Y with parameter p, the probability of a success on any trial, possible values of Y are 1,2,3…