Question
In: Statistics and Probability
Consider the two dependent discrete random variables X and Y . The variable X takes values...
Consider the two dependent discrete random variables X and Y .
The
variable X takes values in {−1, 1} while Y takes values in {1, 2,
3}. We observe that
P(Y =1|X=−1)=1/6
P(Y =2|X=−1)=1/2
P(Y =1|X=1)=1/2
P(Y =2|X=1)=1/4
P(X = 1) = 2/ 5
(a) Find the marginal probability mass function (pmf) of Y .
(b) Sketch the cumulative distribution function (cdf) of Y .
(c) Compute the expected value E(Y ) of Y .
(d) Compute the conditional expectation E[Y |X = 1].
Solutions
orchestra answered 1 year agoRelated Solutions
Question 1: Two jointly distributed discrete random variables Consider two discrete random variables X, Y ,...
Question 1: Two jointly distributed discrete random variables
Consider two discrete random variables X, Y , taking values in {0,
1, 2, 3} each (for a total of 16 possible points). Their joint
probability mass function is given by fXY (x, y) = c · x+1 y+1 .
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Assuming X and Y are discrete random variables, X takes value from the set A =...
Assuming X and Y are discrete random variables, X takes value
from the set A = {x1, x2, x3, …,
xm}，and Y takes value from set B = {y1,
y2, y3, …, yn}, please answer the
following questions
1. If H(X,Y) = H(X) + H(Y), what is the relationship between X
and Y?
2. If I(X,Y) = 0, what is the relationship between X and Y?
3. If I(X;Y) = H(X) = H(Y), what is the relationship between X
and...
Consider the following data for a dependent variable y and two independent variables, x1and x2. x...
Consider the following data for a dependent variable y
and two independent variables, x1and
x2.
x 1
x 2
y
29
13
94
47
10
109
24
17
113
50
16
178
40
6
95
52
20
176
75
7
171
37
13
118
59
14
142
77
17
211
Round your all answers to two decimal places. Enter negative
values as negative numbers, if necessary.
a. Develop an estimated regression equation
relating y to x1.
ŷ = + x1
Predict y...
In this problem there are two random variables X and Y. The random variable Y counts...
In this problem there are two random variables X and Y. The
random variable Y counts how many times we roll the die in the
following experiment: First, we flip a fair coin. If it comes Heads
we set X= 1 and roll a fair die until we get a six. If it comes
Tails, we set X= 0 and roll the die until we get an even number (2,
4 or 6).
a). What are the possible values taken...
1. Assume that X and Y are two independent discrete random variables and that X~N(0,1) and...
1. Assume that X and Y are two independent discrete random
variables and that X~N(0,1) and Y~N(µ,σ2).
a. Derive E(X3) and deduce that E[((Y-µ)/σ)3]
= 0
b. Derive P(X > 1.65). With µ = 0.5 and σ2 = 4.0,
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Given two random variables x and y State of Nature Probability variable x variable y I...
Given two random variables x and y
State of Nature Probability variable x
variable y
I 0.2 18 0
II 0. 2 5 -3
III 0.2 12 15
IV 0.2 4 12
V 0.2 6 1
(i) Calculate the mean and variance of each of these variables
and the covariance between them
(ii) Suppose x and y represent the returns from two assets.
Calculate the mean and variance for the following part folios.
% in x 125 100 75 50...
Consider the following data for a dependent variable y and two independent variables, x2 and x1....
Consider the following data for a dependent variable y and two
independent variables, x2 and x1.
x1 x2 y
30 12 94
46 10 109
24 17 113
50 17 179
41 5 94
51 19 175
75 8 171
36 12 118
59 13 143
77 17 212
Round your all answers to two decimal places. Enter negative
values as negative numbers, if necessary.
a. Develop an estimated regression equation relating y to x1 .
Predict y if x1=45....
Consider the following data for a dependent variable y and two independent variables, x1 and x2.
You may need to use the appropriate technology to answer this question.
Consider the following data for a dependent variable y and two independent variables,
x1 and x2.
x1
x2
y
30
12
93
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
211
The estimated regression equation for these data is
ŷ = −18.89 + 2.02x1 + 4.74x2.
Here, SST = 15,276.0,...
Consider the following data for a dependent variable y and two independent variables, x1 and x2....
Consider the following data for a dependent variable y
and two independent variables, x1 and
x2.
x1
x2
y
30
12
94
47
10
108
25
17
112
51
16
178
40
5
94
51
19
175
74
7
170
36
12
117
59
13
142
76
16
209
The estimated regression equation for these data is ŷ =
−17.02 + 1.99x1 +
4.70x2.
Here, SST = 14,902.9, SSR = 13,773.1,
sb1 =
0.2470, and
sb2 =
0.9480.
(1a) Test...
Consider the following data for a dependent variable y and two independent variables, x1 and x2....
Consider the following data for a dependent variable y
and two independent variables, x1 and
x2.
x1
x2
y
30
13
95
46
10
108
25
18
113
50
16
179
40
5
95
51
20
176
74
7
170
36
12
117
59
13
142
77
16
211
Round your all answers to two decimal places. Enter negative
values as negative numbers, if necessary.
a. Develop an estimated regression equation
relating y to x1.
ŷ =_________ +___________ x1
Predict...
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