Binary random number generation. Given a sequence of U (0, 1) random numbers, obtain and describe an algorithm that generate binary random numbers with the following point masses:

P{X =0}=0.3, P{X =1}=0.7

(a) Find the(theoretical) mean and variance of X.

(b) Use MATLAB U(0,1)random number generator "rand" to generate 10,000 random

numbers with the above distribution.

(c) Compute the average value of the 10,000 random numbers generated. Compare it with

the theoretical mean.

(d) Give the percentages of the numbers generated that are equal to 1, 0, and 1, respec-

tively. Compare them with the point masses and make a comment.

(e) Generate 10,000 random numbers with the above distribution using the companion software PARSE by taking advantage of the relationship between the binomial and

binary distributions and repeat (c)-(d) for these numbers.