Module 5

Question 1

What is a random trial?

Answer 1

any process that has multiple outcomes but where the result on any particular trial is unknown

Question 2

What is the sample space?

Answer 2

the list of possible otucomes in a random trial

Question 3

What is an event?

Answer 3

the outcome you are interested in

Question 4

What is the probability of an event?

Answer 4

the proportion of times that the event would occur if a random trial was repeated many times

Question 5

How do probability distributions utilize the structure of a random trial?

Answer 5

able to provide a compact way of describing the probability of all events, and a tool for calculating probabilities over a range of events

Question 6

What are probability distributions?

Answer 6

functions that describe probability over a range of events.

the probability of observing an outcome within a range of events is the area under the probability distribution functions

Question 7

What properties (3 of them) do probability distributions have?

Answer 7

• they describe the probability for the entire sample space (contains all the necessary info about a random trial)
• the area under the probability distribution always sums to one
• are used to describe both continuous and discrete random variables

Question 8

What are discrete distributions?

Answer 8

probability distributions for discrete random variables

usually shown as a series of vertical bars with no spaces between them. each event gets a seperate bar, and the area of that bar repersents the probability of that event

Question 9

What is continuous distributions?

Answer 9

• probability distributions for continuous random variables
• typically shown as a single curve function of the continuous event
• the area under the curve for a given event range is the probability of observing an outcome in that range

Question 10

What does it mean if the range is zero for a continuous distribution?

Answer 10

then the probability is also zero

Question 11

The probability of a single event in an continuous probability distribution is….?

Answer 11

zero

Question 12

What si the vertical axis for continuous probability distributions?

Answer 12

probability density

Question 13

what is the vertical axis for discrete probability distributions?

Answer 13

probability mass

Question 14

What is the standard normal distribution?

Answer 14

is a special form of the Normal distribution with mean zero and a standard deviation of one.

Question 15

What are the special properties of the standard normal distribution that make it different from a normal distribution?

Answer 15

• mean of the standard normal distribution is zero
• the standard deviation of the standard normal distribution is one
• the x axis is called the z score, which is a scale that measures the number of standard deviations from the mean

Question 16

How to convert a normal distribution to a standard normal distribution?

Answer 16

1. subtract the mean
2. divide by the standard deviation