1. State wether True or false
a. The cumulative distribution function, F(x), of a discrete random variable is the sum of all of the probabilities that are less than or equal to x, where x is a specific value of the discrete random variable, X.
b. P(X = 3) can be written as P(X = 3) = {P(X = 0) + P(X = 1) + P(X = 2) + P(X =3)} – {P(X = 0) + P(X = 1) + P(X = 2)}
c. A cumulative distribution function can be used to find the probability mass function of a discrete random variable.
d. If a random variable, X, has only integer values, then the mean, E(X), will always be an integer.
e. The mean of a discrete random variable is its expected value.
f. If X is a discrete random variable with equal probability at 4, 9, 10, 11, then the mean of X is: 8.5
g. If the variances of two discrete random variables are equal, then the means are equal.
h. The standard deviation of a discrete random variable is the square of its variance