S.Ahmed can you answer the following for me?

S.Ahmed can you answer the following for me?

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ECON 3304.001 Basic Techniques for Economic Research Shidi Wang University of Texas at Dallas, Spring 2015 Problem Set 4 — Due on Monday, Apr. 20th…

S.Ahmed can you answer the following for me?

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ECON 3304.001
Basic Techniques for Economic Research
Shidi Wang
University of Texas at Dallas, Spring 2015
Problem Set 4 — Due on Monday, Apr. 20th
Q1. Consider an experiment where you flip a coin three times. (20 Points)
(a) Find the sample space for this experiment and total number of outcomes. The sample space
is represented by
{}
. (5 Points)
(b) Let X be the random variable which is the number of tails and x be an actual value of the
random variable. The total number of outcomes is denoted as n. There are four possible
outcome x, namely 0, 1, 2, and 3. Find the probability that the random variable X equals x and
fill in the following table. (10 Points)
Pr (X = x)
Number of ways that the number of tails equals x
Total number of possible outcomes
Pr (X = 0)
Pr (X = 1)
Pr (X = 2)
Pr (X = 3)
Total
(c) Graph the probability distribution function. (Hint: use the information from the table in (b)
with
Pr (X = x)
on the y-axis and x on the x-axis) (5 Points)
Q2. Consider an experiment where you roll a pair of dice. Each outcome is mutually exclusive
and equally likely to occur. Let X be the random variable which is the sum of two dice. Let x be
an actual value of the random variable. (35 Points)
(a) The following table shows all possible values of the random variable. Complete the table.
(10 Points)
1
2
3
4
5
6
1
2
3
6
4
5
6
12
(b) Write down the sample space. (6 Points)
(c) Find the total number of possibilities. (3 Points)
(d) Fill in the following table. (11 Points)
x
2
3
4
5
6
7
8
9
10
11
12
Pr (X = x)
(e) Graph the probability distribution function. (Hint: use the information from the table in (d)
with
Pr (X = x)
on the y-axis and x on the x-axis) (5 Points)

View the Answer

Q3. Consider the data in the following table. The data shows the number of hours that eight
students in a class study per week. (35 Points)
Hours that eight students study per week
12
13
19
18
15
15
11
17
(a) Let the random variable Y be the hours that students in a class study per week. Complete
the following table. (10 Points)
y
i
(y
i
− μ
Y
)
(y
i
− μ
Y
)
2
(y
i
− μ
Y
)
3
(y
i
− μ
Y
)
4
12
13
19
18
15
15
11
17
Sum
(b) Find the mean of the data. (3 Points)
(c) Find the mode. (2 Points)
(d) Find
the medIan.
(2 Points)
(e) Find the standard deviation of the data and interpret your result. (6 Points)
(f) Find the skewness of the data and interpret your result. (6 Points)
(g) Find the kurtosis of the data and interpret your result. (6 Points)
Q4. For each of the following distributions, give an example of a situation where you could use
this distribution. (10 Points)
(a) Discrete Uniform Distribution (2.5 Points)
(b) Binomial Distribution (2.5 Points)
(c) Negative Binomial Distribution (2.5 Points)
(d) Poisson Distribution (2.5 Points)

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