Determine whether each of the following statements is true or false.
(a) If X is a continuous random variable then the cumulative distribution function (cdf) of X must be continuous.
True
False
(b) If X is a continuous random variable that follows a uniform distribution then the mean and median of X must be equal.
True
False
(c) If X is a continuous random variable that follows an exponential distribution, we will always have that the mean of X is greater than the median of X.
True
False
(d) If X is a continuous random variable with probability density function (pdf) f(x), then for any number c we have that P(X=c) is f(c).
True
False
(e) If X is a continuous random variable that follows a normal distribution, we will always have that the mean of X is greater than the median of X.
True
False