Santa Monica College Marginal Probability Distributions Questions Hey guys, I attached 5 pictures down below pls check them before bidding on this assignme

Santa Monica College Marginal Probability Distributions Questions Hey guys, I attached 5 pictures down below pls check them before bidding on this assignment, I need detailed solutions and the answers from you. (I expect all the answers to be right, if you don’t believe you can get all the questions right do not bid on this assignment)Thank you already! Question 7
A study was conducted to investigate the relationship between two variables X and Y.
The frequencies observed were as in the table below.
Y=5 Y=10 Y=15
X=0/30 15
17.5
X=117.5 45
15
|X=20
15
15
(i) Calculate the marginal probability distributions, f(X) and f(Y).
(ii) Calculate E(X) and E(Y).
Calculate Var (X) and Var (Y).
(iv)
Compute the conditional expectation of X given that Y = 15
ie E(X/Y=15).
(v)
Are X and Y independent? Explain your answer.
(vi)
Calculate the covariance between X and Y – ie Cov (X,Y).
(vii)
Calculate the correlation coefficient between the two variables X
and Y and explain what it measures.
Question 8
The demand curve for a particular good and the total cost function are given as follows:
Demand:
P= 24 – Q
TCQ)= *Q2-6Q? +33Q +15
Total Cost:
(a) Find the Total Revenue function and also the Marginal Revenue function
for this good.
(b) On the same diagram, sketch both the demand function and the marginal revenue function
ensuring that you indicate all intercepts.
(c) Find the profit function.
(d) Calculate the firm’s profit-maximising level of output ensuring that you check the second order
conditions for a profit maximum.
(e) What are the values of profit, price and total revenue at the profit-maximising output level.
(f) If the firm were to maximise revenue rather than profit, find the quantity produced, the price
charged and the amount of profit and total revenue that would result and comment on you
results.
Question 9
Given the following demand and supply functions for three interdependent commodities.
Q = 19 – 4P +P, +2P
e
S
=-
A
— 5 + 3P
A
A
Q = 23 + P -5PB
D
B
+P
Q* =- 8 + 6P
?
B
Q’ = 15 +2P +P,-3P
o’=- 11 +3 P.
(a)
By setting supply equal to demand in each market, find the equations for the
equilibrium prices.
(b)
Ensure that the variables are in the same order in each equation and write the
equations in the matrix form Ap = b. (where p is the price vector and b is the vector
of constants)
(c)
Use Cramer’s rule OR the inverse method to solve for the three equilibrium
prices.
(d)
Find the equilibrium quantities.
(e
)
Comment on which goods are substitutes and which goods are complements and
explain your answers.
Areas under the Standard Normal (Z)
Distribution Curve
From 0 to Z
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.01
0.0000
0.0040
0.0080
0.0120
0.0160
0.0199 0.0239 0.0279 0.0319 0.0359
0.1
0.0398
0.0438
0.0478
0.0517
0.0557
0.2
0.0793
0.0832
0.0871
0.0910
0.0948
0.3
0.1179
0.1217
0.1255
0.1293
0.1331
0.4
0.1554
0.1591
0.1628
0.1664
0.1700
0.5
0.1915
0.1950
0.1985
0.2054
0.2019
0.2357
0.6
0.2257
0.2291
0.2324
0.2389
0.7
0.2580
0.2611
0.2642
0.2673
0.2704
0.8
0.2881
0.2910
0.2939
0.2967
0.0596 0.0636 0.0675 0.0714 0.0753
0.0987 0.1026 0.1064 0.1103 0.1141
0.1368 0.1406 0.1443 0.1480 0.1517
0.1736 0.1772 0.1808 0.1844 0.1879
0.2088 0.2123 0.2157 0.2190 0.2224
0.2422 0.2454 0.2486 0.2517 0.2549
0.2734 0.2764 0.2794 0.2823 0.2852
0.3023 0.3051 0.3078 0.3106 0.3133
0.3289 0.3315 0.3340 0.3365 0.3389
0.3531 0.3554 0.3577 0.3599 0.3621
0.3749 0.3770 0.3790 0.3810 0.3830
0.3944 0.3962 0.3980 0.3997 0.4015
0.4115 0.4131 0.4147 0.4162 0.4177
0.4265 0.4279 0.4292 0.4306 0.4319
0.4394 0.4406 0.4418 0.4429 0.4441
0.4505 0.4515 0.4525 0.4535 0.4545
0.9
0.3159
0.3186
0.3238
0.2995
0.3264
0.3508
0.3729
0.3212
0.3461
1.0
0.3413
0.3438
0.3485
1.1
0.3643
0.3665
0.3686
0.3708
1.2
0.3849
0.3869
0.3888
0.3907
1.3
0.4032
0.4192
0.4332
0.4049
0.4207
0.4345
0.4066
0.4222
0.4082
0.4236
1.4
0.3925
0.4099
0.4251
1.5
0.4357
0.4382
0.4370
0.4484
1.6
0.4452
0.4463
0.4474
0.4495
1.7
0.4554
0.4573
0.4582
0.4591
0.4564
0.4649
1.8
0.4641
0.4656
0.4664
0.4671
1.9
0.4713
0.4772
0.4719
0.4778
0.4726
0.4783
0.4732
0.4788
0.4738
0.4793
2.0
2.1
0.4821
0.4826
0.4830
0.4834
0.4838
2.2
0.4861
0.4864
0.4868
0.4871
0.4875
2.3
0.4893
0.4896
0.4898
0.4901
0.4904
2.4)
0.4918
0.4920
0.4922
0.4925
0.4927
2.5
0.4938
0.4940
0.4943
2.6
0.4953
0.4955
0.4966
0.4941
0.4956
0.4967
0.4945
0.4959
0.4969
2.7
0.4957
0.4968
0.4977
0.4965
0.4974
2.8
0.4977
0.4976
0.4982
0.4599 0.4608 0.4616 0.4625 0.4633
0.4678 0.4686 0.4693 0.4699 0.4706
0.4744 0.4750 0.4756 0.4761 0.4767
0.4798 0.4803 0.4808 0.4812 0.4817
0.4842 0.4846 0.4850 0.4854 0.4857
0.4878 0.4881 0.4884 0.4887 0.4890
0.4906 0.4909 0.4911 0.4913 0.4916
0.4929 0.4931 0.4932 0.4934 0.4936
0.4946 0.4948 0.4949 0.4951 0.4952
0.4960 0.4961 0.4962 0.4963 0.4964
0.4970 0.4971 0.4972 0.4973 0.4974
0.4978 0.4979 0.4979 0.4980 0.4981
0.4984 0.4985 0.4985 0.4986 0.4986
0.4989 0.4989 0.4989 0.4990 0.4990
0.4992 0.4992 0.4992 0.4993 0.4993
0.4994 0.4994 0.4995 0.4995 0.4995
0.4996 0.4996 0.4996 0.4996 0.4997
0.4997 0.4997 0.4997 0.4997 0.4998
0.4998 0.4998 0.4998 0.4998 0.4998
0.4999 0.4999 0.4999 0.4999 0.4999
0.4999 0.4999 0.4999 0.4999 0.4999
0.4999 0.4999 0.4999 0.4999 0.4999
0.5000 0.5000 0.5000 0.5000 0.5000
2.9
0.4981
0.4984
3.0
0.4975
0.4982
0.4987
0.4991
0.4993
0.4987
0.4983
0.4988
0.4991
0.4988
3.1
0.4987
0.4991
0.4994
0.4990
0.4992
3.2
0.4994
0.4994
0.4993
0.4995
3.3
0.4995
0.4995
0.4996
0.4996
3.4
0.4997
0.4997
0.4997
0.4997
0.4998
0.4997
0.4998
3.5
0.4998
0.4998
3.6
0.4999
0.4999
0.4998
0.4999
0.4998
0.4999
0.4998
0.4999
0.4999
3.7
0.4999
3.8
0.4999
0.4999
0.4999
0.4999
0.4999
0.5000
0.4999
3.9
0.5000
0.5000
0.5000
0.5000
Areas under the Standard Normal (Z)
Distribution Curve
From 0 to Z
0
0.01
0.02
0.03
0.04
0.05 0.06 0.07
0.08
0.09
0.0
0.0000
0.0040
0.0080
0.0120
0.1
0.0398
0.0478
0.0517
0.0438
0.0832
0.0160
0.0557
0.0948
0.1331
0.2
0.0793
0.0910
0.0871
0.1255
0.3
0.1179
0.1293
0.4
0.1554
0.1217
0.1591
0.1950
0.1628
0.1664
0.1700
0.5
0.1915
0.1985
0.2019
0.2054
0.6
0.2291
0.2324
0.2257
0.2580
0.71
0.2642
0.2611
0.2910
0.2357
0.2673
0.2967
0.2389
0.2704
0.2995
0.8
0.2939
0.2881
0.3159
0.9
0.3186
0.3212
0.3238
0.3264
1.0
0.3413
0.3438
0.3485
0.3508
0.3461
0.3686
1.1
0.3643
0.3665
0.3708
1.2
0.3907
0.3849
0.4032
0.4192
0.3869
0.4049
0.3888
0.4066
0.3729
0.3925
0.4099
0.4251
1.3
0.4082
1.4
0.4207
0.4222
0.4236
1.5
0.4332
0.4345
0.4357
0.4370
0.4382
1.6)
0.4452
0.4463
0.4474
0.4484
0.4495
1.7
0.4554
0.4564
0.4573
0.4582
0.4591
1.8
0.4641
0.4649
0.4656
0.4664
0.4671
1.9
0.4713
0.4719
0.4732
0.4738
0.4726
0.4783
0.0199 0.0239 0.0279 0.0319 0.0359
0.0596 0.0636 0.0675 0.0714 0.0753
0.0987 0.1026 0.1064 0.1103 0.1141
0.1368 0.1406 0.1443 0.1480 0.1517
0.1736 0.1772 0.1808 0.1844 0.1879
0.2088 0.2123 0.2157 0.2190 0.2224
0.2422 0.2454 0.2486 0.2517 0.2549
0.2734 0.2764 0.2794 0.2823 0.2852
0.3023 0.3051 0.3078 0.3106 0.3133
0.3289 0.3315 0.3340 0.3365 0.3389
0.3531 0.3554 0.3577 0.3599 0.3621
0.3749 0.3770 0.3790 0.3810 0.3830
0.3944 0.3962 0.3980 0.3997 0.4015
0.4115 0.4131 0.4147 0.4162 0.4177
0.4265 0.4279 0.4292 0.4306 0.4319
0.4394 0.4406 0.4418 0.4429 0.4441
0.4505 0.4515 0.4525 0.4535 0.4545
0.4599 0.4608 0.4616 0.4625 0.4633
0.4678 0.4686 0.4693 0.4699 0.4706
0.4744 0.4750 0.4756 0.4761 0.4767
0.4798 0.4803 0.4808 0.4812 0.4817
0.4842 0.4846 0.4850 0.4854 0.4857
0.4878 0.4881 0.4884 0.4887 0.4890
0.4906 0.4909 0.4911 0.4913 0.4916
0.4929 0.4931 0.4932 0.4934 0.4936
0.4946 0.4948 0.4949 0.4951 0.4952
0.4960 0.4961 0.4962 0.4963 0.4964
0.4970 0.4971 0.4972 0.4973 0.4974
0.4978 0.4979 0.4979 0.4980 0.4981
0.4984 0.4985 0.4985 0.4986 0.4986
0.4989 0.4989 0.4989 0.4990 0.4990
0.4992 0.4992 0.4992 0.4993 0.4993
0.4994 0.4994 0.4995 0.4995 0.4995
0.4996 0.4996 0.4996 0.4996 0.4997
0.4997 0.4997 0.4997 0.4997 0.4998
0.4998 0.4998 0.4998 0.4998 0.4998
0.4999 0.4999 0.4999 0.4999 0.4999
0.4999 0.4999 0.4999 0.4999 0.4999
0.4999 0.4999 0.4999 0.4999 0.4999
0.5000 0.5000 0.5000 0.5000 0.5000
2.0
0.4772
0.4778
0.4788
0.4793
2.1
0.4821
0.4826
0.4830
0.4834
0.4838
2.2
0.4861
0.4871
0.4864
0.4896
0.4868
0.4898
2.3
0.4893
0.4901
2.4
0.4918
0.4920
0.4922
0.4925
2.5
0.4938
0.4953
2.6
0.4940
0.4955
0.4966
0.4941
0.4956
0.4967
0.4875
0.4904
0.4927
0.4945
0.4959
0.4969
0.4977
0.4984
0.4988
0.4992
2.7
0.4943
0.4957
0.4968
0.4977
0.4983
0.4965
2.8
0.4975
0.4976
2.9
0.4982
0.4974
0.4981
0.4987
0.4990
3.0
0.4987
0.4988
0.4982
0.4987
0.4991
0.4993
3.1
0.4991
0.4991
3.2
0.4993
0.4994
0.4994
0.4994
3.3
0.4995
0.4995
0.4995
3.4
0.4997
0.4998
0.4997
0.4998
0.4998
0.4997
0.4998
0.4996
0.4997
0.4998
3.51
0.4996
0.4997
0.4998
0.4999
0.4999
3.6
0.4998
0.4999
0.4999
3.7
0.4999
0.4999
0.4999
0.4999
3.8)
0.4999
0.4999
0.4999
0.4999
0.4999
3.9
0.5000
0.5000
0.5000
0.5000
0.5000

Purchase answer to see full
attachment