Problem 1: Comparing means and standard deviations

The two histograms below shows tow distributions. The first distribution is of a variable X. The second distribution is of a random variable Y = X + 10.

  1. Based on the histogram, what is the mean of X?
  2. Based on the histogram, what is the mean of Y?
  3. If the standard deviation of X is equal to 1, what is the standard deviation of Y?

Problem 2: Stock portfolio

A stock portfolio is a collection of stocks a person owns. The total value of a stock portfolio depends on the total number of shares you purchase as well as the price of the stock (which varies over time). Let X be the price of a single share of a certain company’s stock at a point in time. Suppose the mean return on this stock is $25/share, while the standard deviation is $5/share. If you buy 100 shares of this stock, then the total value of your portfolio is given by Y = 100X. What is the mean return on your portfolio (Y)? What is the standard deviation of returns on your portfolio?