Are the following statements true or false?
(a) The variance of a random variable is measured in the same units as the random variable.
(b) In a diving competition, the scores awarded by judges for a particular type of dive have an expected value of 78 with a standard deviation of 5. If the scores are doubled so that they can be compared with scores from an easier type of dive, the new scores will have an expected value of 156 and a standard deviation of 10.
(c) The variance of the difference between two independent random variables cannot be smaller than the larger of their two variances.
(d) If a continuous random variable has a symmetric probability density function, then the mean and the median are identical.
(e) If X is a continuous random variable, then P(X ≥ v) = P(X > x) for any value of x.
(f) If X is a discrete random variable, then P(X ≥.x) = P(X > x) for any value of x.