Stats 2 week 3 important questions

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1. Q4The pmf of a random variable X is c|ccc x 0 2 4 , P(X=x) 0.3 0.4 0.3 Find Var(…
2. Q5The pmf of a random variable X is c|cccc x 1 3 5 7 , P(X=x) 0.3 0.2 0.4 0.1 Find …
3. Q6The pmf of a random variable X is c|ccc x -2 0 2 , P(X=x) 0.3 0.3 0.4 Find E(3X-3).
4. Q7The pmf of a random variable X is c|ccc x 0 1 2 , P(X=x) 0.4 0.2 0.4 Find Var(…
5. Q8The pmf of a random variable X is c|cccc x 2 4 6 8 , P(X=x) 0.3 0.5 0.1 0.1 Find the stan…
6. Q9The pmf of a random variable X is c|ccc x 1 2 3 , P(X=x) 0.3 0.3 0.4 Find E[(X-1)2…
7. Q10The pmf of a random variable X is c|ccc x -1 1 3 , P(X=x) 0.4 0.4 0.2 Find E(X2)-…
8. Q11The pmf of a random variable X is c|ccc x 0 5 10 , P(X=x) 0.2 0.6 0.2 Find E(X).
9. Q12The pmf of a random variable X is c|cccc x 10 20 30 40 , P(X=x) 0.5 0.3 0.1 0.1 Find E(X)…
10. Q13The pmf of a random variable X is c|cccc x 0 1 2 3 , P(X=x) 0.4 0.1 0.2 0.3 Find E(X2).
11. Q14The pmf of a random variable X is c|cccc x 1 2 3 4 , P(X=x) 0.1 0.2 0.2 0.5 Find …
12. Q15The pmf of a random variable X is c|cccc x -1 0 1 2 , P(X=x) 0.2 0.2 0.2 0.4 Find …
13. Q16The pmf of a random variable X is c|ccc x 0 2 4 , P(X=x) 0.2 0.7 0.1 Find E(2X+1).
14. Q17The pmf of a random variable X is c|cccc x 1 3 5 7 , P(X=x) 0.2 0.2 0.5 0.1 Find …
15. Q18The pmf of a random variable X is c|ccc x -2 0 2 , P(X=x) 0.5 0.2 0.3 Find the standard de
16. Q19The pmf of a random variable X is c|ccc x 0 1 2 , P(X=x) 0.3 0.3 0.4 Find E[(X-3)2…
17. Q20The pmf of a random variable X is c|cccc x 2 4 6 8 , P(X=x) 0.3 0.2 0.4 0.1 Find E(X…
18. Q21The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.25 0.2 0.1 , 1 0.1 0.2 0.15 …
19. Q22The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.1 0.1 0.15 , 1 0.05 0.15 0.1 , 2 0.1 …
20. Q23The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.4 0.25 , 1 0.1 0.25 Find E(XY).
21. Q24The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.15 0.15 , 1 0.15 0.2 , 2 0.15 0.2 …
22. Q25The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.35 0.15 0.25 , 1 0.05 0.05 0.15 ar…
23. Q26The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.2 0.1 0.1 , 1 0.1 0.1 0.1 , 2 0.1 0…
24. Q27The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.25 0.25 , 1 0.15 0.35 Find E(X).
25. Q28The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.15 0.3 , 1 0.15 0.15 , 2 0.1 0.15 …
26. Q29The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.05 0.05 0.2 , 1 0.2 0.3 0.2 …
27. Q30The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.1 0.1 0.15 , 1 0.1 0.05 0.05 , 2 0.2 …
28. Q31The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.55 0.25 , 1 0.1 0.1 Find the correla…
29. Q32The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.35 0.1 , 1 0.05 0.2 , 2 0.2 0.1 …
30. Q33The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.2 0.25 0.05 , 1 0.2 0.1 0.2 …
31. Q34The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.05 0.1 0.15 , 1 0.2 0.05 0.1 , 2 0.15…
32. Q35The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.4 0.2 , 1 0.2 0.2 Find E(XY).
33. Q36The joint pmf of X and Y is c|cc X Y 0 1 , 0 0.05 0.05 , 1 0.15 0.35 , 2 0.2 0.2 …
34. Q37The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.05 0.15 0.2 , 1 0.2 0.2 0.2 …
35. Q38The joint pmf of X and Y is c|ccc X Y 0 1 2 , 0 0.1 0.1 0.15 , 1 0.15 0.05 0.2 , 2 0.15…
36. Q39E(X)=1 and E(Y)=6. Find E(2X+4Y).
37. Q40X and Y are independent with Var(X)=1 and Var(Y)=5. Find Var(X+Y).
38. Q41X and Y are independent with Var(X)=4 and Var(Y)=4. Find Var(X-Y).
39. Q42X and Y are independent with Var(X)=4 and Var(Y)=5. Find Var(3X-4Y).
40. Q43X and Y are independent with E(X)=1 and E(Y)=3. Find E(XY).
41. Q44What is the expected value of the sum of the numbers shown when 5 fair dice are thrown?
42. Q45A fair coin is tossed 40 times. Let X be the number of heads. Using indicator variables fo
43. Q46E(X)=3 and E(Y)=5. Find E(3X+4Y).
44. Q47X and Y are independent with Var(X)=5 and Var(Y)=4. Find Var(X+Y).
45. Q48X and Y are independent with Var(X)=2 and Var(Y)=4. Find Var(X-Y).
46. Q49X and Y are independent with Var(X)=5 and Var(Y)=2. Find Var(2X-4Y).
47. Q50X and Y are independent with E(X)=6 and E(Y)=1. Find E(XY).
48. Q51A fair coin is tossed 20 times. Let X be the number of heads. Using indicator variables fo
49. Q52In a game you win ₹20 with probability 1/4 and lose ₹10 otherwise. What is your expected g
50. Q53A fair die is thrown. You receive ₹ equal to the number shown if it is at least 6, and not
51. Q544 people each throw a fair die. A person wins ₹60 if the die shows 6. What is the expected
52. Q55The number of complaints received in an hour is 0, 1, 2 or 3 with probabilities 0.1, 0.2,
53. Q56In a game you win ₹20 with probability 1/2 and lose ₹10 otherwise. What is your expected g
54. Q57A fair die is thrown. You receive ₹ equal to the number shown if it is at least 3, and not
55. Q586 people each throw a fair die. A person wins ₹60 if the die shows 6. What is the expected
56. Q59The number of complaints received in an hour is 0, 1, 2 or 3 with probabilities 0.3, 0.2,
57. Q60The number of complaints received in an hour is 0, 1, 2 or 3 with probabilities 0.4, 0.1,
58. Q61Cov(X,Y)=-1. Find Cov(3X+1,-3Y-5).
59. Q62Var(X)=4, Var(Y)=4 and Cov(X,Y)=-3. Find Var(X+Y).
60. Q63Var(X)=4, Var(Y)=9 and Cov(X,Y)=5. Find the correlation coefficient (2 decimal places).
61. Q64Cov(X,Y)=4. Find Cov(-2X+1,-3Y-5).
62. Q65Var(X)=16, Var(Y)=25 and Cov(X,Y)=4. Find Var(X+Y).
63. Q66Var(X)=16, Var(Y)=9 and Cov(X,Y)=4. Find Var(X-Y).
64. Q67Var(X)=16, Var(Y)=25 and Cov(X,Y)=4. Find the correlation coefficient (2 decimal places).
65. Q68Cov(X,Y)=-3. Find Cov(3X+1,2Y-5).
66. Q69Var(X)=16, Var(Y)=25 and Cov(X,Y)=5. Find Var(X+Y).
67. Q70Var(X)=4, Var(Y)=25 and Cov(X,Y)=-3. Find Var(X-Y).
68. Q71Var(X)=9, Var(Y)=25 and Cov(X,Y)=2. Find the correlation coefficient (2 decimal places).
69. Q72Select all the true statements.
70. Q73Which of the following statements about expectation and variance are true?
71. Q74Choose the correct statements.
72. Q75Select every true statement.
73. Q76Which statements hold in general?
74. Q77Mark all the correct statements.
75. Q78Which of these are true?
76. Q79Read each statement and select the true ones.
77. Q80The bar chart shows the pmf of a random variable X. Find E(X).
78. Q81Refer to the figure. The bar chart shows the pmf of a random variable X. Find E(X).
79. Q82The bar chart shows the pmf of a random variable X. Find Var(X) (3 decimal places).
80. Q83The bar chart shows the pmf of a random variable X. Find E(2X+1).
81. Q84The bar chart shows the pmf of a random variable X. Find E(X). Select all the true stateme
82. Q85Look at the diagram given. The bar chart shows the pmf of a random variable X. Find E(X).
83. Q86Refer to the figure. The bar chart shows the pmf of a random variable X. Find Var(X) (3 de
84. Q87The bar chart shows the pmf of a random variable X. Find E(3X+1).
85. Q88Study the figure carefully. The bar chart shows the pmf of a random variable X. Find E(X).
86. Q89Use the picture shown. The bar chart shows the pmf of a random variable X. Find E(X).
87. Q90Look at the diagram given. The bar chart shows the pmf of a random variable X. Find Var(X)
88. Q91Refer to the figure. The bar chart shows the pmf of a random variable X. Find E(2X+1).
89. Q92Refer to the figure. The bar chart shows the pmf of a random variable X. Find E(X). Select
90. Q93From the diagram, answer this. The bar chart shows the pmf of a random variable X. Find E(
91. Q94Study the figure carefully. The bar chart shows the pmf of a random variable X. Find Var(X
92. Q95Look at the diagram given. The bar chart shows the pmf of a random variable X. Find E(2X+1
93. Q96A fair die is thrown once. Find the variance of the number shown (3 decimal places).
94. Q97Two fair dice are thrown. Let M be the larger of the two numbers. Find E(M) (3 decimal pla
95. Q98Two fair dice are thrown. Let S be the smaller of the two numbers. Find E(S) (3 decimal pl
96. Q99A random variable X takes the value 1 with probability p=0.3 and 0 otherwise. Find Var(X)
97. Q100Ten people leave their hats at a party and the hats are returned at random. Let X be the n