Unit 5 Flashcards
what is random behavior?
unpredictable in the short-run, but has a regular and predictable distribution in the long-run
for example, if we only have 10 samples of an x value then it will be unpredictable, but in the long run if we have 1000000 samples then its more predictable because the shape starts to get created (probability)
when do we use a density curve?
continuous quantitative variables
when do we call a phenomenon random?
if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions
what is the probability of any outcome of a random phenomenon?
the proportion of times the outcome would occur in an infinitely long series of trials
what is the difference between proportions and probability?
proportion: known or observed value. present tense.
probability: theoretical value of a proportion after an infinitely long series of trials that can never be observed. it relates to future events.
what is the mathematical model used to describe random behavior?
probability model
what are two components of the probability model?
a list of possible outcomes
a probability for each outcome
what is probability?
the probability that an event occurs is the long run proportion of times we would see that event occur in a very long series of trials
what is a sample space?
(S) of a random phenomenon is the set of all possible outcomes.
ex. if we toss a coin twice S={HH,HT,TH,TT}
what is an event?
any subset of outcomes in the sample space.
ex. the event sum is 9 for rolling two dice would be
B={36,45,54,63}
what is the complement of an event?
(A^c) of an event (A) consists of all outcomes in the sample space which are not contained in A.
basically, the complement is everything opposite of A.
random variable
a variable whose value is a numerical outcome of a random phenomenon
what are the two types of random variables?
discrete and continuous
what is a discrete random variable?
has a countable number of possible outcomes
what is a continuous random variable?
takes on all possible values in an interval
ex. weight or distance
probability distribution
gives the values of some variable, as well as the probability of each value
what does the probability distribution of a random variable X tell us ?
tells us what values X can take and how to assign probabilities to those values
if X~N(µ, σ) we say that X follows a normal probability distribution
what is sampling distribution of the sample mean x̄?
x̄~N( μ, σ/ √n)
are averages less or more variable than individual observations?
less variable (therefore, are skinny and tall in a density curve)
what happens to the sampling distribution of x̄ as n increases?
the sampling distribution of x̄ approaches a normal distribution
what is the central limit theorem state?
if a variable represents a sample mean, then the sampling distribution of the variable is approximately normal when n is high
when is it safe to apply the central limit theorem?
when n is bigger than 30
what is true population proportion?
p
its a parameter
what is the sample proportion?
p̂
is a statistic and an estimate for p
when talking about proportions what needs to be met?
n x p needs to be bigger than 10
n (1-p) needs to be bigger than 10
what is probability?
the probability that an event occurs is the long run proportion of times we would see that event occur in a very long series of trials
when would the answer be approximate?
when using the central limit theorem
its approximate because we will never get the exact values regardless of how much n increases.
