Stats 2 week 2 important questions

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1. Q4The joint pmf of X and Y is c|cc X Y 1 2 , 0 0.2 0.4 , 1 0.3 0.1 Are X and Y indepe…
2. Q5The joint pmf of X and Y is c|cc X Y 1 2 , 0 0.18 0.42 , 1 0.12 0.28 Are X and Y in…
3. Q6The joint pmf of X and Y is c|ccc X Y 1 2 3 , 0 0.2 0.05 0.15 , 1 0.25 0.3 0.05 arra…
4. Q7The joint pmf of X and Y is c|ccc X Y 1 2 3 , 0 0.15 0.06 0.09 , 1 0.15 0.06 0.09 , 2 0…
5. Q8The joint pmf of X and Y is c|cc X Y 1 2 , 0 0.15 0.1 , 1 0.5 0.25 Are X and Y inde…
6. Q9The random variables X and Y are independent. Their joint pmf is c|ccc X Y 1 2 3 , 0 0.16
7. Q10The random variables X and Y are independent. Their joint pmf is c|ccc X Y 1 2 3 , 0 0.12
8. Q11The random variables X and Y are independent. Their joint pmf is c|ccc X Y 1 2 3 , 0 0.04
9. Q12The random variables X and Y are independent. Their joint pmf is c|ccc X Y 1 2 3 , 0 0.05
10. Q13The random variables X and Y are independent. Their joint pmf is c|ccc X Y 1 2 3 , 0 0.2 0
11. Q14The random variables X and Y are independent. Their joint pmf is c|ccc X Y 1 2 3 , 0 0.25
12. Q15X and Y are independent with P(X=2)=0.4 and P(Y=0)=0.2. Find P(X=2,Y=0).
13. Q16X and Y are independent with P(X=1)=0.3 and P(Y=0)=0.6. Find P(X=1,Y=0).
14. Q17X and Y are independent with P(X=3)=0.3 and P(Y=1)=0.3. Find P(X=3,Y=1).
15. Q18X and Y are independent with P(X=2)=0.5 and P(Y=0)=0.7. Find P(X=2,Y=0).
16. Q19X and Y are independent with P(X=3)=0.4 and P(Y=0)=0.6. Find P(X=3,Y=0).
17. Q20X and Y are independent with P(X=3)=0.3 and P(Y=1)=0.6. Find P(X=3,Y=1). Select all the tr
18. Q21X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.5, 0.1, 0.4; Y ta
19. Q22X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.8, 0.1, 0.1; Y ta
20. Q23X and Y are independent. X takes the values 0, 1 with probabilities 0.5, 0.5; Y takes the
21. Q24X and Y are independent. X takes the values 0, 1, 2, 3 with probabilities 0.2, 0.4, 0.3, 0
22. Q25X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.5, 0.2, 0.3; Y ta
23. Q26X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.5, 0.3, 0.2; Y ta
24. Q27X and Y are independent. X takes the values 0, 1 with probabilities 0.6, 0.4; Y takes the
25. Q28X and Y are independent. X takes the values 0, 1, 2, 3 with probabilities 0.2, 0.3, 0.3, 0
26. Q29X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.2, 0.5, 0.3; Y ta
27. Q30X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.4, 0.3, 0.3; Y ta
28. Q31X and Y are independent. X takes the values 0, 1 with probabilities 0.7, 0.3; Y takes the
29. Q32X and Y are independent. X takes the values 0, 1, 2, 3 with probabilities 0.1, 0.1, 0.5, 0
30. Q33X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.1, 0.6, 0.3; Y ta
31. Q34X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.3, 0.2, 0.5; Y ta
32. Q35X and Y are independent. X takes the values 0, 1 with probabilities 0.3, 0.7; Y takes the
33. Q36X and Y are independent. X takes the values 0, 1, 2, 3 with probabilities 0.2, 0.1, 0.5, 0
34. Q37X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.2, 0.3, 0.5; Y ta
35. Q38X and Y are independent. X takes the values 0, 1, 2 with probabilities 0.3, 0.2, 0.5; Y ta
36. Q39X and Y are independent. X takes the values 0, 1 with probabilities 0.5, 0.5; Y takes the
37. Q40X and Y are independent. X takes the values 0, 1, 2, 3 with probabilities 0.1, 0.2, 0.2, 0
38. Q41X takes the values -1, 0, 1, 2 with probabilities 0.1, 0.3, 0.1, 0.5. Find P(X2=4) (2 deci
39. Q42X takes the values -2, -1, 1, 2 with probabilities 0.2, 0.1, 0.4, 0.3. Find P(|X|2) (2 dec
40. Q43X takes the values -1, 0, 1, 2 with probabilities 0.4, 0.2, 0.2, 0.2. Let Y=2X+1. Find P(Y
41. Q44X takes the values -2, -1, 1, 2 with probabilities 0.4, 0.2, 0.2, 0.2. Let Z=X2-1. How man
42. Q45X takes the values -1, 0, 1, 2 with probabilities 0.3, 0.3, 0.1, 0.3. Find P(X2=4) (2 deci
43. Q46X takes the values -2, -1, 1, 2 with probabilities 0.3, 0.3, 0.3, 0.1. Find P(|X|2) (2 dec
44. Q47X takes the values -1, 0, 1, 2 with probabilities 0.3, 0.3, 0.2, 0.2. Let Y=2X+1. Find P(Y
45. Q48X takes the values -2, -1, 1, 2 with probabilities 0.5, 0.1, 0.3, 0.1. Let Z=X2-1. How man
46. Q49Two independent events: A happens with probability 1/5 and B with probability 1/2. Find th
47. Q50A fair coin is tossed 5 times and a fair die is thrown once, independently. Find the proba
48. Q51A fair die is thrown twice independently. Find the probability that the first throw gives
49. Q52Each of two independent machines fails in a day with probability 1/3. Find the probability
50. Q53Two independent events: A happens with probability 2/3 and B with probability 1/4. Find th
51. Q54A fair coin is tossed 6 times and a fair die is thrown once, independently. Find the proba
52. Q55A fair die is thrown twice independently. Find the probability that the first throw gives
53. Q56Each of two independent machines fails in a day with probability 1/4. Find the probability
54. Q57Two independent events: A happens with probability 1/2 and B with probability 1/3. Find th
55. Q58Select all the true statements.
56. Q59Which of the following statements about independence are true?
57. Q60Choose the correct statements.
58. Q61Select every true statement about independent random variables.
59. Q62Which statements hold?
60. Q63Mark all the correct statements.
61. Q64Which of these are true?
62. Q65Read each statement and select the true ones.
63. Q66The bar chart shows the pmf of X. The independent variable Y has the same pmf (so P(Y=y)=P
64. Q67The bar chart shows the pmf of Z=X+Y. Find P(Z2) (2 decimal places).
65. Q68The bar chart shows the pmf of X. The independent variable Y has the same pmf (so P(Y=y)=P
66. Q69Refer to the figure. The bar chart shows the pmf of Z=X+Y. Find P(Z2) (2 decimal places).
67. Q70Refer to the figure. The bar chart shows the pmf of X. The independent variable Y has the
68. Q71Look at the diagram given. The bar chart shows the pmf of Z=X+Y. Find P(Z2) (2 decimal pla
69. Q72Look at the diagram given. The bar chart shows the pmf of X. The independent variable Y ha
70. Q73Study the figure carefully. The bar chart shows the pmf of Z=X+Y. Find P(Z2) (2 decimal pl
71. Q74The bar chart shows the pmf of X. The independent variable Y has the same pmf (so P(Y=y)=P
72. Q75Use the picture shown. The bar chart shows the pmf of Z=X+Y. Find P(Z2) (2 decimal places)
73. Q76The independent random variables X and Y take the values 0, 1, 2. X has probabilities 0.2,
74. Q77The independent random variables X and Y take the values 1, 2, 3. X has probabilities 0.3,
75. Q78The independent random variables X and Y take the values 0, 1. X has probabilities 0.5, 0.
76. Q79The independent random variables X and Y take the values 1, 2, 3, 4. X has probabilities 0
77. Q80The independent random variables X and Y take the values 2, 4, 6. X has probabilities 0.2,
78. Q81The independent random variables X and Y take the values 0, 1, 2, 3. X has probabilities 0
79. Q82The independent random variables X and Y take the values 1, 3, 5. X has probabilities 0.2,
80. Q83The independent random variables X and Y take the values 0, 2. X has probabilities 0.8, 0.
81. Q84The independent random variables X and Y take the values 0, 1, 2 with the pmfs (0.3, 0.4,
82. Q85The independent random variables X and Y take the values 1, 2, 3 with the pmfs (0.5, 0.3,
83. Q86The independent random variables X and Y take the values 0, 1 with the pmfs (0.7, 0.3) for
84. Q87The independent random variables X and Y take the values 1, 2, 3, 4 with the pmfs (0.4, 0.
85. Q88The independent random variables X and Y take the values 0, 1, 2, 3 with the pmfs (0.2, 0.
86. Q89The independent random variables X and Y take the values 2, 3, 4 with the pmfs (0.4, 0.3,
87. Q90X takes the values 0, 1 with probabilities 0.3, 0.7, and Y (independent of X) takes the va
88. Q91X takes the values 0, 2 with probabilities 0.2, 0.8, and Y (independent of X) takes the va
89. Q92X takes the values 1, 2 with probabilities 0.5, 0.5, and Y (independent of X) takes the va
90. Q93X takes the values 0, 1, 2 with probabilities 0.2, 0.3, 0.5, and Y (independent of X) take
91. Q94X takes the values 1, 3 with probabilities 0.5, 0.5, and Y (independent of X) takes the va
92. Q95The joint pmf of X and Y (each taking the values 1, 2, 3) is p(x,y)=c, ,xy, for a suitable
93. Q96The joint pmf of X and Y (each taking the values 1, 2, 3) is p(x,y)=c, ,(x+y), for a suita
94. Q97The joint pmf of X and Y (each taking the values 1, 2, 3) is p(x,y)=c, ,x2y, for a suitabl
95. Q98The joint pmf of X and Y (each taking the values 1, 2, 3) is p(x,y)=c, ,(x2+y), for a suit
96. Q99The joint pmf of X and Y (each taking the values 1, 2, 3) is p(x,y)=c, ,(x+1)(y+2), for a
97. Q100The joint pmf of X and Y (each taking the values 1, 2, 3) is p(x,y)=c, ,(2x+y), for a suit