Discrete and Continuous Random Variables Vocab + Rules

random variable

a variable whose value is a numerical outcome of a random phenomenon

discrete random variable

a countable number of possible values

how do you find the expected value of a discrete probability distribution (or the mean)

multiply each possible value by its probability then add all products

how do you find the variance of a discrete probability distribution

subtract the mean from each possible value, square that, multiply that by the individual probability of that value, then add all those values together

how do you find the standard deviation of a discrete probability distribution

take the square root of the variance.

what does the linear transformation rule for means say

if x is a random variable and a and b are constants, then the mean of the transformed variable a+bx is given by E(a +bx) = a + E(x)b

what orders of operations can be done with means

the means can be added, subtracted, or multiplied together but cannot be divided

if x and y are INDEPENDENT random variables, what order of operation can you do with variances

the variances can ONLY be added

what is the rule for the variance of a transformed variable

given the equation a +bx, you can transform the variance with the equation Var(a + bx) = b²Var(x) where b is the slope

continuous random variable

takes all values in an interval of numbers, infinite number of outcomes

how to calculate the probability of a continuous random variable

take the area under the density curve

what is a the probability for any individual outcome of a continuous random variable

always 0

what is a uniform curve

A type of probability distribution where all outcomes are equally likely within a given interval (both height and length are 1)