Discrete random variables

Random variables whose values can be listed but the list can be infinite

Continuous random variables

Random variables that can take on any value in an interval and are
not restricted to any list

Discrete probability distributions

They must all be 0-1 and the sum of the probabilities must equal to 1

Mean of discrete random variable (expected value)

Multiply each possibly value by its probability and then add the products

Standard deviation of discrete random variable

The square root of the variance

Probability density curve

The curve used to describe the distribution of a continuous random
variable and tells us what proportion of the population falls within
any given interval

Area under the probability density curve

Proportion of the population whose values are between a and b
Probability that a randomly selected value from the population will
be between a and b

Properties of normal distributions

#NAME?

Empirical rule

68% is within one standard deviation
95% is within two standard deviations
99.7% is within three standard deviations

Standard normal distribution

Has a mean 0 and standard deviation 1, letter z indicates a value on
the horizontal axis and it is called a z-score

Z?

The z-score with an area of ? to its right

Z score formula

X minus mean divided by standard deviation

Finding a normal value using table A.2

- Sketch a normal curve, label value x to be found and shade in and
label the given area
- If the given area is on the right, subtract it from 1 to get the
area on the left
- Find the Z-score corresponding to that area
- Obtain the value by computing x= ? + z?