Thread: Check my work regarding probability, mean, variance, standard deviation?

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?

Originally Posted by 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?

a) is correct. I haven't bothered doing (b). Your answers to (c) are consistent with your answers to (b) and your answers to (d) are consistent with those in (c).