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ECON 3303.1

Atul A. Dar Test 1 October 13, 2020

Posted: 11:20am

Answer any two (and only two) questions. Each is worth 10 points. You must show the method you use to arrive at

your answers.

Your answers must be uploaded to the folder TEST 1 on Dropbox in Brightspace no later than 1: 05pm, October 13.

Question 1 Parts A and B are unrelated

A. The conditional probability distributions of a random variable Y are given below.

f(y|x=2)

f (y|x=4)

f(y|x=7)

f(y|x=10)

10/11

5/11

1/11

4/11

5/16

1/7

2/11

5/16

4/7

6/16

2/7

Means

5.4545

9.5455

20.625

21.4286

The marginal distributions of X is:

x: 2 4 7 10

f(x): 0.11 0.22 0.32 0.35

1. Use the information provided to obtain the unconditional means of X and Y; that is, the means of the marginal

distributions of these variables. Do not answer this by trying to obtain f(x,y). (4 points)

2. Are X and Y statistically independent? Explain. (2 points)

B. If X and Y are two independent random variables with means 30 and 60 respectively, and variances 28 and

25 respectively, (i) find the mean and variance of 2X -3Y. (2 points)

(ii) Can you estimate the extent to which X and Y are linearly related? If yes, what is your estimate and what

does it tell us; if not, why not? Explain briefly. (2 points)

Question 2 Parts A and B unrelated

A. Suppose X is the weight of boxes of butter (in kilograms) shipped between two countries. It is known that E(X) =25

and var(X)=4.

1. What is the mean and variance of Y = 0.5X – 12.5. Show your work. (3 points)

2. What is the probability that a box drawn randomly from a shipment would have a weight (a) greater than 26.5 kg.

(b) less than 24 kg? (c) between 22kg and 25 kg (3 points)

B. Consider the following probability distribution:

x: 0 1 2 3 4

f(x): b 2b 3b 4b 5b

Determine the value of the constant b, and then find the mean and variance of X. (4 points)

Question 3 (10 points)

Suppose that the equity return (Y) and size (X) of firms in a certain population are jointly distributed. It is believed that

the conditional mean of return is linearly related to size: E(Y|X)= β

+β

X. You are given the following information for a

sample 34 companies:

N = 34, Σ(x

- x

)

= 223,495, Σ(y

-)

= 31,949.7, Σ(x

- x

)(y

-) = -5686.6, Σx

=1439.2, and Σy

= 360.7

Note: Y is measured in percent, while size is measured by company assets ($ billion).

A. Obtain the sample covariance σ̂

and obtain a measure of the degree to which Y and X are correlated. (3 points)

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Atul A. Dar ECON 3303.1 Test 1 October 13, 2020 Posted: 11:20am Answer any two (and only two) questions. Each is worth 10 points. You must show the method you use to arrive at your answers. Your answers must be uploaded to the folder TEST 1 on Dropbox in Brightspace no later than 1: 05pm, October 13. Question 1 Parts A and B are unrelated A. The conditional probability distributions of a random variable Y are given below. y f(y|x=2) f (y|x=4) f(y|x=7) f(y|x=10) 5 10/11 5/11 0 0 10 1/11 4/11 5/16 1/7 20 0 2/11 5/16 4/7 30 0 0 6/16 2/7 Means 5.4545 9.5455 20.625 21.4286 The marginal distribut ...
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