Question

Topic 3 (About CLT and Bayes'Theorem: 10 marks] A particle moves along the line in a random walk. That is, the particle starts at the origin (position 0) and moves either 2 units to the right or I unit to the left in independent steps. If the particle moves to the right with probability 2/3, its movement at the ih step is a random variable X, with distribution P(x+2)-2/3 P(X,-)=13 The position of the particle after 400 steps is the sum of these random movements, 400 Use the central limit theorem to find the approximate probability that the position of the particle after 400 steps is at least 100 to the right. HINT: An equlvalent random experiment 四回1400 draws 61. (1 mark) Find an equivalent random experiment by completing the above box. A) 2 &-without replacement ( is the number of Number 2 tickets in box) B) 7-3&7 without replacement C)?-2&2- with replacement D?-1&- with replacement 62. (1 mark) Find E[Xi]. A)-1 B)0 C)1 D)2 E)0.33 F0.67. 63. (1 mark) Find E[X30 A)-3 B)0.S C)I D)9.2 E)0.33 F) 0.67 64. (1 mark) Find VIXi]. A)-1 B)0 C D)2 B)0.33 F)0.67. 65.(2 marks) Find P[100 3 Y] is ween 0 and 0.20 D) between 6. (2 marks) Find Pl-l A) between 0 0 B) between 0.20 and 0.40 C) between 0.40 and 0.60 0.60 and 0.80 E) between 0.80 and 1. Xi+X: 3 is and 0.20 B) between 0.20 and 0.40 C) between 0.40 and 0.60 and 0.80 E) between 0.80 and 1 67.0

Answer 1

Solving first 4 sub-parts by HomeworkLib policy

61)

this is with replacement

hence option C/D) is correct

option C) is correct

62)

E(X1) = 2 *2/3 -1 *1/3 = 1

option C)

63)

E(X30)= E(X1) = 1

option C)

64)

E(X^2) = 2/3 * 2^2 + 1/3 * 1 = 3

V(X1) = E(X^2)- (E(X))^2

= 3 - 1^2 = 2

option D) is correct