Ch 6 Random variables Flashcards
random variable
takes numerical values that describe the outcomes of some chance process
discrete
random variable that means countable
mean of a discrete random variable aka ?
expected value
when finding the expected value, should you round your answer?
No, do not round
variance is aka?
standard deviation squared
continuous random variable X
takes all values in an interval of numbers (is not countable)
when multiplying each value of a random variable by a positive # b, what happens?
measures of spread & center is multiplied by b
shape of distribution does NOT change
multiplying random variable by constant b multiplies the variance by b^2
when adding each value of a random variable by the same positive # a what happens?
measures of center is added by a
shape and spread doesnt change
mean of difference =
mean of the sum =
difference of the means
sum of the means
variance of the sum =
variance of the difference =
sum of the variances
sum of the variances
what needs to be true to add the variances
the random variables must be independent
never subtract variances, only add-> never add standard deviations
4 requirements for binomial distribution
each observation = 2 categories success or fail
fixed number n of observations
n observations are all independent
probability of success, call it p, is the same for each observation (BINS)
2 types of probability distributions for discrete random variables
geometric or binomial
binomialpdf
probability distribution function for exactly with fixed number trials p(x=___)
binomcdf
cumulative distribution function for inequality w/ fixed number of trials P(x>__)
mean of binomial formula
n times p equals expected value
how many successes you have on average
s.d. of binomal
sqrt np(1-p)
difference btwn geometric and binomial
geometric has no fixed number, go until successful
how many 3s in 10 rolls
binomial
how long until an ace is drawn?
neither not independent
histogram is always what shape for geometric?
right skewed
histogram is always what shape for binomial?
roughly symmetric
