random variables, their means and variances

Question 1

what are the random variables and their probability models?

Answer 1

quantitative result of a random experiment, denoted by a capital letter

discrete rv: there is a certain set of possible outcomes

continuous rv: can take on any value from an interval of numbers (usually a quantity)

Question 2

P(X=x) defines

Answer 2

the probability distribution for discrete variables

Question 3

determining the mean (or expected value) of a discrete rv

Answer 3

can be determined as the weighted sum of all possible outcomes. mean is E(X) = sum (xi . pi)

Question 4

are there transformations of the mean?

Answer 4

yes, learn them

Question 5

determine variance of a discrete random variable

Answer 5

variance measures how far random variables tend from the mean. This distance is X - mewX

Question 6

variance of X

Answer 6

E(X Squared) - (mew X) squared

Question 7

are there transformations of variance?

Answer 7

yes, learn them

Question 8

special case for binomial random variables

Answer 8

mew = E(X) = np

var(X) = np(1-p)

sigma = square root (np(1-p))