 # Statistics Questions

### Question 1:

By referring to the image to the right, evaluate the matrix C = A*B

Matrix multiplication is performed as follows:

C =   ((A(1,1) * B(1,1) + A(1,2) * B(2,1))          ((A(1,1) * B(1,2) + A(1,2) * B(2,2))

((A(2,1) * B(1,1) + A(2,2) * B(2,1))          ((A(2,1) * B(1,2) + A(2,2) * B(2,2))

C =   (1 * 1 + 2 * 0)         (1 * 1 + 2 * 2)

(3 * 1 + 4 * 0)         (3 * 1 + 4 * 2)

C =   1       5

3      11

### Question 2:

Evaluate the expectation and the variance of the distribution given by the probability mass function for the random variable x taking on the values in the set {1, 4, 10} displayed in the image to the right.

Expectation is calculated according to the equation:

= ∑(x_i * p(x = x_i))

= (x_1 * p(x = x_1)) + (x_2 * p(x = x_2)) + (x_3 * p(x = x_3))

= (1 * 0.3) + (4 * 0.2) + (10 * 0.5)

= 5.4

Variance is calculated according to the equation:

= ∑(x_i - expectation)2

= (x_1 - 5.4)2 + (x_2 - 5.4)2 + (x_3 - 5.4)2

= (1 - 5.4)2 + (4 - 5.4)2 + (10 - 5.4)2

= 42.6

### Question 3:

What does GLM stand for?

The General Linear Model is the basis of the majority of statistical analysis techniques.

### Question 4:

Which of the following is the equation for linear regression?

The formula for linear regression is the same as that of a straight line because in linear regression you are trying to find a linear relationship between the dependent variable y and the independent variable x.