Question 5 [3x3 pts + 3 pts + 3x3pts] a. Consider the matrix 13 = 0 (i) Compute A3 (ii) Compute As (ii) What is A? ? b. Consider them x m diagonal matrix Am with elements (a;]. Based on your results from parts (a), what is Am where n is a positive integer? C. Consider the matrix R2 = ( 1) (i) Compute R? (ii) Compute R2 (ii) What is RZ ? Question 6 [3x3 pts] A throw of a regular die yields the numbers 1, 2, ..., 6, each with probability 1/6. Find the mean, variance, and standard deviation of the numbers obtained. Question 7 [2x3pts + 2x3pts] Let x be a continuous random variable that can take any value x 2 0. A quantity is said to be exponentially distributed if it takes values between x and x + dx with probability P(x)dx = Ae-x/2 dx, where a and A are constants. a. Find the value of A that makes P(x) a well-defined continuous probability distribution. (i. e. S P(x) dx = 1). b. Show that the mean value (x) = 1. c. Find the variance and the standard deviation. 2/2