4.80 Find the mean of the sum. Figure 4.12 (page 245) displays the density curve of the sum Y = X1 + X2 of two independent random numbers, each uniformly distributed between 0 and 1.

  1. (a) The mean of a continuous random variable is the balance point of its density curve. Use this fact to find the mean of Y from Figure 4.12.

  2. (b) Use the same fact to find the means of X1 and X2. (They have the density curve pictured in Figure 4.9, page 240.) Verify that the mean of Y is the sum of the mean of X1 and the mean of X2.