Ch.6 Random Variable

x and y are independent random variables

- knowing the value of one variable tells you nothing about the value of the other -the variance of the sum of two independent random variables is the sum of their variances -the variance of the difference of two independent random variables is the sum of their variances

multiplying (dividing) a random variable by a positive constant b

does not change the shape of the probability distribution

discrete random variable

has a fixed set of possible values with gaps between them

adding a positive constant a to (subtracting a from) a random variable

increases (decreases) the mean of the random variable by a but does not affect its standard deviation or the shape of its probability distribution

probability distribution

of a random variable X tells us what the possible values of X are and how probabilities are assigned to those values

linear transformation

of a random variable involves adding or subtracting a constant a, multiplying or dividing by a constant b, or both. y=a +bx center: mean y= a + B( mean x) spread: standard deviation y= abs b (stand. dev. x)

standard deviation

square root of the variance

continuous random variable

takes all values in some interval of numbers -a density curve describes the probability distribution of a continuous random variable. The probability of any event is the area under the curve above the values that make up the event

random variable

takes numerical values determined by the outcome of a chance process

variance of a random variable

the average squared deviation of the values of the variable from their mean (X1-meanx)^2(P1) + (x2-meanx)^2 (p2)

mean of a random variable

the balance point of the probability distribution histogram or density curve. Because the mean is the long-run average value of the variable after many repititions of the chance process, it is also known as the expected value -If X is a discrete random variable, the mean is the average of the values of X, weighed by its probability x1p1+x2p2+x3p3

x and y are two random variables

the mean of the sum of two random variables is the sum of their means -the mean of the difference of two random variables is the difference of their means