module 5 Flashcards
random trial
- Any process with many possible outcomes but the result on any particular trial is unknown
sample space
- set of all possible outcomes of a random trial
- typically shown within {}
what is the outcome you are interested in called in probability
- event
- can be a single element in or any subset of the sample space
random trials can have _____ or ______ variables
Continuous or discrete
t or f: probabilities are formally shown as percentages
false, shown as proportions
probability distributions
- describe probability over a range of events
- use structures of a random trial to provide compact way of describing probability of all events
properties of a probability distribution
- describe the probability for the entire sample space, categorizes all possible outcomes
- area under the probability distribution always sums to one
- used to describe both cont. and discrete random variables
area under the probability distribution always sums to _______
one
discrete distributions
- probability distributions for discrete random variables
- whole numbers
- shown as a series of vertical bars w no spaces between, with events getting separate bars and bar area=event probability
- vertical axis=probability mass
- looks like a histogram
vertical axis of discrete distributions are called ______
probability mass
continuous distribution
- looks like a hill
- for continuous random variables (not whole numbers, decimals )
- shown as a single curve
- area under the curve = probability of observing and outcome in that range
- vertical axis=probability density
vertical axis of continuous distributions are called ______
probability density
if the range is 0 for continuous distributions, the probability is _____
0
t or f: the probability of a single event in continuous and discrete distributions is always zero
false, the probability of a single event in a continuous distribution is always zero
what can be used to answer the following questions:
what is the probability of observing an outcome over a given range of the variable?
What range of the variable is consistent with a given probability?
probability distributions
standard normal distribution is a special form of the Normal distribution with mean _____ and a standard deviation of _____.
zero, one
the x axis on a standard normal distribution is call the ______
z-score, measures the number of SDs from the mean
what do standard normal distributions look like
- distributions but it is separated into slices that are one SD wide along the z-score axis
how to convert to the standard normal distribution
- z=(x-μ)/σ where z=value of interest on the standard normal distribution, x= value of interest on the og distribution
- subtract the mean
- divide by the standard deviation
The probability and range description in a problem are used to calculate a ______ from the standard Normal distribution
z-score
The ______ (μ), ________(σ) and ________ (x) in a problem are used to calculate a corresponding z-score from the equation z=(x-μ)/σ.
mean, standard deviation, value of interest
what are probability distributions used for
- calculate probability corresponding to a range of events
- calculate a range of events corresponding to a probability