Statistics and Probability Answers

Let A be square matrix which of the following statements is correct?

A. A-A^T and (-A^TA^T) are symmetric

B. A+A^T is symmetric and (-A^TA^T) is skew symmetric

C.(-AA^T) is symmetric

D. A^TA and A+A^T are symmetric

Consider the following data:

x 3 7 8 10 12

y 7 10 12 12 16

a) calculate the covariance and correlation coefficient between variables x and y

b) identify the relationship between 2 variables

c) compare the coefficent of variation (CV) between both variables

yamaha is giving away a free motorbike to one of their 155 best customers. In this group, 55 are women, 70 are married and 40 are married men. The marital status can be only married or single.

(a) what is the probability that the motorbike will be awarded to someone who is single?

(b) given the winner is married, what is the probability that it is a woman?

1.    10 fair die are rolled. Find the expected value of the sum of the faces showing.

2.    An urn contains 2 red chips and 3 white chips.

a.    Two are drawn out at random without replacement. Let X denote the number of red chips in the sample. Calculate Var(X).

b.    Calculate Var(X) if the sampling is done with replacement.

1.    Ajouin and Genie are a happy couple and have 4 lovely children. Is it more likely they will have two boys and two girls or three of the same sex and one of the other? Assume that the probability of a child being a boy is 0.5 and that the births are independent events. (5 points)

2.    A fair die is rolled 4 times. Let the random variable X denote the number of sixes that appear. Find F_X(x). (5 points)