Stats 2 week 4 important questions

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1. Q4The density of X is f(x)=c, ,(1-x2) for -1<= x<= 1 and 0 otherwise. Find the value of c (3
2. Q5The density of X is f(x)=c, ,x(2-x) for 0<= x<= 2 and 0 otherwise. Find the value of c (3
3. Q6The density of X is f(x)=c, ,(x+1) for 0<= x<= 3 and 0 otherwise. Find the value of c (3 d
4. Q7The density of X is f(x)=c, ,e-x for 0<= x< and 0 otherwise. Find the value of c (3 decima
5. Q8The density of X is f(x)=c, ,x3 for 0<= x<= 2 and 0 otherwise. Find the value of c (3 deci
6. Q9The density of X is f(x)=c, ,(3-x) for 0<= x<= 3 and 0 otherwise. Find the value of c (3 d
7. Q10The density of X is f(x)=c for 2<= x<= 7 and 0 otherwise. Find the value of c (3 decimal p
8. Q11The density of X is f(x)=c, ,x for 0<= x<= 4 and 0 otherwise. Find the value of c (3 decim
9. Q12The density of X is f(x)=c, ,(4-x2) for -2<= x<= 2 and 0 otherwise. Find the value of c (3
10. Q13The density of X is f(x)=c, ,x for 0<= x<= 2 and 0 otherwise. Find 1/c (3 decimal places).
11. Q14The density of X is f(x)=c, ,x2 for 0<= x<= 3 and 0 otherwise. Find 1/c (3 decimal places)
12. Q15The density of X is f(x)=c, ,(2x+1) for 0<= x<= 1 and 0 otherwise. Find 1/c (3 decimal pla
13. Q16The density of X is f(x)=c, ,(1-x2) for -1<= x<= 1 and 0 otherwise. Find 1/c (3 decimal pl
14. Q17The density of X is f(x)=x/2 for 0<= x<= 2 and 0 otherwise. Find P(0<= X<= 1) (3 decimal p
15. Q18The density of X is f(x)=x2/9 for 0<= x<= 3 and 0 otherwise. Find P(3/4<= X<= 39/16) (3 de
16. Q19The density of X is f(x)=2x+1/2 for 0<= x<= 1 and 0 otherwise. Find P(1/4<= X<= 5/8) (3 de
17. Q20The density of X is f(x)=34(1-x2) for -1<= x<= 1 and 0 otherwise. Find P(-1<= X<= 1/2) (3
18. Q21The density of X is f(x)=34x(2-x) for 0<= x<= 2 and 0 otherwise. Find P(1/2<= X<= 5/4) (3
19. Q22The density of X is f(x)=29(3-x) for 0<= x<= 3 and 0 otherwise. Find P(3/4<= X<= 39/16) (3
20. Q23The density of X is f(x)=15 for 2<= x<= 7 and 0 otherwise. Find P(2<= X<= 9/2) (3 decimal
21. Q24The density of X is f(x)=x3/4 for 0<= x<= 2 and 0 otherwise. Find P(1<= X<= 2) (3 decimal
22. Q25The density of X is f(x)=x2/9 for 0<= x<= 3 and 0 otherwise. Find P(0<= X<= 3) (3 decimal
23. Q26The density of X is f(x)=2x+1/2 for 0<= x<= 1 and 0 otherwise. Find P(1/2<= X<= 3/4) (3 de
24. Q27The density of X is f(x)=34(1-x2) for -1<= x<= 1 and 0 otherwise. Find P(-1<= X<= 0) (3 de
25. Q28The density of X is f(x)=29(3-x) for 0<= x<= 3 and 0 otherwise. Find P(3/4<= X<= 3) (3 dec
26. Q29The density of X is f(x)=15 for 2<= x<= 7 and 0 otherwise. Find P(13/4<= X<= 41/8) (3 deci
27. Q30The density of X is f(x)=x3/4 for 0<= x<= 2 and 0 otherwise. Find P(1/2<= X<= 5/4) (3 deci
28. Q31The density of X is f(x)=x/2 for 0<= x<= 2 and 0 otherwise. Find P(1<= X<= 2) (3 decimal p
29. Q32The density of X is f(x)=x2/9 for 0<= x<= 3 and 0 otherwise. Find P(3/4<= X<= 15/8) (3 dec
30. Q33The density of X is f(x)=2x+1/2 for 0<= x<= 1 and 0 otherwise. Find P(0<= X<= 1/2) (3 deci
31. Q34The density of X is f(x)=34(1-x2) for -1<= x<= 1 and 0 otherwise. Find P(- 1/2<= X<= 1/4)
32. Q35The density of X is f(x)=34x(2-x) for 0<= x<= 2 and 0 otherwise. Find P(1/2<= X<= 13/8) (3
33. Q36The density of X is f(x)=29(3-x) for 0<= x<= 3 and 0 otherwise. Find P(3/2<= X<= 21/8) (3
34. Q37The distribution function of X is F(x)=x2/4 for 0<= x<= 2 (0 below 0 and 1 above 2). Find
35. Q38The distribution function of X is F(x)=x3/27 for 0<= x<= 3. Find P(3/4<X<= 9/4) (3 decimal
36. Q39The distribution function of X is F(x)=x2+x/2 for 0<= x<= 1. The density is f(x)=F(x). Fin
37. Q40The distribution function of X is F(x)=x-2/5 for 2<= x<= 7. Find P(X>9/2) (3 decimal place
38. Q41The distribution function of X is F(x)=x2/4 for 0<= x<= 2. Find the median of X (2 decimal
39. Q42The distribution function of X is F(x)=x3/27 for 0<= x<= 3 (0 below 0 and 1 above 3). Find
40. Q43The distribution function of X is F(x)=x2+x/2 for 0<= x<= 1. Find P(1/4<X<= 3/4) (3 decima
41. Q44The distribution function of X is F(x)=x-2/5 for 2<= x<= 7. The density is f(x)=F(x). Find
42. Q45The distribution function of X is F(x)=x2/4 for 0<= x<= 2. Find P(X>1) (3 decimal places).
43. Q46The distribution function of X is F(x)=x3/27 for 0<= x<= 3. Find the median of X (2 decima
44. Q47The distribution function of X is F(x)=x2+x/2 for 0<= x<= 1 (0 below 0 and 1 above 1). Fin
45. Q48The distribution function of X is F(x)=x-2/5 for 2<= x<= 7. Find P(13/4<X<= 23/4) (3 decim
46. Q49The distribution function of X is F(x)=x2/4 for 0<= x<= 2. The density is f(x)=F(x). Find
47. Q50The distribution function of X is F(x)=x3/27 for 0<= x<= 3. Find P(X>3/2) (3 decimal place
48. Q51The density of X is f(x)=x/2 for 0<= x<= 2 and 0 otherwise. Find E(X) (3 decimal places).
49. Q52The density of X is f(x)=x2/9 for 0<= x<= 3 and 0 otherwise. Find Var(X) (3 decimal places
50. Q53The density of X is f(x)=2x+1/2 for 0<= x<= 1 and 0 otherwise. Find E(X) (3 decimal places
51. Q54The density of X is f(x)=34(1-x2) for -1<= x<= 1 and 0 otherwise. Find Var(X) (3 decimal p
52. Q55The density of X is f(x)=34x(2-x) for 0<= x<= 2 and 0 otherwise. Find E(X) (3 decimal plac
53. Q56The density of X is f(x)=29(3-x) for 0<= x<= 3 and 0 otherwise. Find Var(X) (3 decimal pla
54. Q57The density of X is f(x)=15 for 2<= x<= 7 and 0 otherwise. Find E(X) (3 decimal places).
55. Q58The density of X is f(x)=x3/4 for 0<= x<= 2 and 0 otherwise. Find Var(X) (3 decimal places
56. Q59X is uniformly distributed on [0,10]. Find P(X<= 2) (2 decimal places).
57. Q60X is uniformly distributed on [2,8]. Find E(X). Select all the true statements about the v
58. Q61X is uniformly distributed on [1,5]. Find Var(X) (3 decimal places).
59. Q62X is uniformly distributed on [-3,3]. Given that X>0, find the probability that X>1 (2 dec
60. Q63X is uniformly distributed on [0,15]. For what value of t is P(X<= t)=0.6 (2 decimal place
61. Q64X is uniformly distributed on [0,4]. Find P(X<= 1) (2 decimal places).
62. Q65X is uniformly distributed on [10,30]. Find E(X).
63. Q66X is uniformly distributed on [2,14]. Find Var(X) (3 decimal places).
64. Q67X is uniformly distributed on [0,12]. Given that X>6, find the probability that X>9 (2 dec
65. Q68X is uniformly distributed on [0,10]. For what value of t is P(X<= t)=0.6 (2 decimal place
66. Q69Select all the true statements.
67. Q70Which of the following statements about continuous random variables are true?
68. Q71Choose the correct statements.
69. Q72Select every true statement.
70. Q73Which statements hold?
71. Q74Mark all the correct statements.
72. Q75Which of these are true?
73. Q76Read each statement and select the true ones.
74. Q77The figure shows the density of X: constant on an interval starting at 0 and zero elsewher
75. Q78The figure shows the density of X: a straight line from the origin up to the marked point,
76. Q79The figure shows a flat density on [0,4] (zero elsewhere), with the right end marked. Find
77. Q80The figure shows a triangular density on [0,4] with its peak at (2,1/2) marked. Find P(X>=
78. Q81The figure shows the density of X: constant on an interval starting at 1 and zero elsewher
79. Q82Refer to the figure. The figure shows the density of X: a straight line from the origin up
80. Q83Refer to the figure. The figure shows a flat density on [0,4] (zero elsewhere), with the r
81. Q84The figure shows a triangular density on [0,4] with its peak at (2,1/2) marked. Find P(X>=
82. Q85Refer to the figure. The figure shows the density of X: constant on an interval starting a
83. Q86The figure shows the density of X: a straight line from the origin up to the marked point,
84. Q87Look at the diagram given. The figure shows a flat density on [0,4] (zero elsewhere), with
85. Q88The figure shows a triangular density on [0,8] with its peak at (4,1/4) marked. Find P(X>=
86. Q89The figure shows the density of X: constant on an interval starting at 0 and zero elsewher
87. Q90Look at the diagram given. The figure shows the density of X: a straight line from the ori
88. Q91The figure shows a flat density on [0,2] (zero elsewhere), with the right end marked. Find
89. Q92Refer to the figure. The figure shows a triangular density on [0,4] with its peak at (2,1/
90. Q93The density of X is f(x)=2x1 for 0<= x1 and 0 otherwise. Find P(X>12) (3 decimal places).
91. Q94The density of X is f(x)=3x2 for 0<= x1 and 0 otherwise. Find E(X) (3 decimal places).
92. Q95The density of X is f(x)=4x3 for 0<= x1 and 0 otherwise. Find P(X>12) (3 decimal places).
93. Q96The density of X is f(x)=5x4 for 0<= x1 and 0 otherwise. Find E(X) (3 decimal places).
94. Q97The density of X is f(x)=6x5 for 0<= x1 and 0 otherwise. Find P(X>12) (3 decimal places).
95. Q98The density of X is f(x)=7x6 for 0<= x1 and 0 otherwise. Find E(X) (3 decimal places).
96. Q99The density of X is f(x)=8x7 for 0<= x1 and 0 otherwise. Find P(X>12) (3 decimal places).
97. Q100The density of X is f(x)=9x8 for 0<= x1 and 0 otherwise. Find E(X) (3 decimal places).