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**Mattpd** S is the sample space and it include all possible 2x2 binary matrices. Each entry (i.e. 0 or 1) both have the same probability of appearing, 1/2. Let X be a random variable that equals the determinant of much a matrix.

a) How many matrices are in S?

2^4 = 16

b) Make a list of all the matrices and find the determinants.

I did this part and found there are 10 with 0 as the determinate, 3 with 1 as determinate, and 3 with -1 as determinate.

c) What is the probability of each value of X?

0 is 10/16

-1 is 3/16

1 is 3/16

d) Find the mean, variance, and std deviation.

mean=0

variance=6/16

std dev= sqrt(6)/4

Look ok?