STA – 本题是一个利用STA进行练习的代做, 对STA的流程进行训练解析, 是比较典型的STA等代写方向

R语言 统计代做 代写统计

Student Number

STA 256 f2019 LEC0101 Test 3

Tutorial Section (Circle One)
TUT0101 TUT0102 TUT0103 TUT0104 TUT
Mon. 3-4 Mon. 4-5 Mon. 5-6 Mon. 6-7 Wed. 4-
DH 2080 DH 2080 IB 360 IB 240 IB
Ali Dashvin Dashvin Ali Marie
TUT0106 TUT0107 TUT0108 TUT0109 TUT
Wed. 5-6 Fri. 9-10 Fri. 10-11 Fri. 10-11 Fri. 11-
IB 360 IB 200 DH 2070 DV 3093 DH 2070
Marie Crendall Ali Cendall Ali
TUT0111 TUT0112 TUT0113 TUT0114 TUT
Fri. 11-12 Fri. 12-1 Fri. 4-5 Fri. 5-6 Fri. 6-
DV 3093 DV 2070 DV 3093 IB 360 IB 360
Crendall Crendall Karan Karan Karan
Wed. 11-12 Wed. 12-
DH 2070 IB 260
Ana Ana
Question Value Score
1 20
2 15
3 25
4 20
5 20
Total = 100 Points
  1. Let the random variablesXandY have joint density
fX,Y(x,y) =


24 xy For 0x 1 , 0 y1 andx+y 1
0 Otherwise
(a) (3 points) Sketch the region of thex,yplane where the joint density is non-zero.
(b) (8 points) Find the marginal densityfX(x). Show your work. Be sure to specify
where the density is non-zero.
(c) (1 point) You know the marginal densityfY(y) by symmetry. Just write it down.
Be sure to specify where the density is non-zero.

(d) (2 points) AreXandY independent? Answer Yes or No and briefly justify your answer.

(e) (6 points) Give the conditional densityfY|X(y|x). Be sure to specify where the
density is non-zero.
  1. (15 points) Let X and Y be independent, discrete random variables. Show that E{g(X)h(Y)}= E{g(X)}E{h(Y)}. BecauseX andY are discrete, you will add rather than integrating to do this question. Be very clear about where you use inde- pendence. Draw an arrow pointing to where you use independence, and write This is where I use independence.
  1. LetX 1 andX 2 be independent normal random variables with= 0 and^2 = 1. Let Y 1 =X 1 X 2 andY 2 =X 1 +X 2.
(a) (10 points) Calculate the joint density ofY 1 andY 2. Show your work, andcircle
your final answer. The next part of this question will go better if you simplify
your answer.

Continue Question 3 if necessary.

(b) (10 points) Find the marginal density ofY 1 =X 1 X 2.

(c) (5 points) The distribution ofY 1 is one of the common distributions on the
formula sheet. Identify it by name and give the value(s) of the parameter(s).
  1. LetXhave a binomial distribution with parametersnand.
(a) (12 points) Derive the moment-generating function ofX. Show your work.Cir-
cle your final answer. You can check your answer on the formula sheet, but if
you force your answer to come out right by making a convenient mistake, you
will get a zero for this part.
(b) (8 points) Use the moment-generating function to findE(X). Show your work.
Circle your answer. If your answer to part (a) does not agree with the formula
sheet, use the formula sheet.
  1. (20 points) LetX 1 ,X 2 andX 3 be independent random variables, where
X 1 Gamma (= 1,= 1) X 2 Gamma (= 2,= 1) X 3 Gamma (= 3,= 1)
Find the distribution ofY =X 1 +X 2 +X 3. Show your work. It is one of the common
distributions on the formula sheet. Name the distribution and give the values of the
Total Marks = 100 points