Suppose that x has a discrete uniform distribution on the integers 0 through 9. determine the mean, variance, and standard deviation of the random variable equals 5x=y

With 10 integers available, has PMF



We're interested in the statistics of the new random variable . To do this, we need to know the PMF for . This isn't too hard to find.



Since the PMF for gives a value of whenever is an integer between 0 and 9, it follows that must also be an integer for the PMF to give the identical value of . This means



Now the mean (expectation) is




The variance would be






The standard deviation is the square root of the variance, so you have