Question

A data set consists of the four integers: 1,2,3,4 what is the probability that if a bootstrap sample is taken, the following sequence of numbers is drawn, in order: (3,1,1,3) 0.00832050 0.01256028 0.00390625

Answer 1

) ㅗ ར Am A dada set consists of four integers'. 1,2,3, 4. In a boods drup sampling, eveny number, hoy equal chance of being in the sample and sampling is dones with replacement so prob of integer i (i=1,2, 3,4 l, being in sample= Ā so the prob that if a boodstrap. sample is takers, the sequence of numbers in drawn in order & 3, 1, 1,31 = 114 x 14 x 7 8 x 1 / 4 =0.00390625 The number of boodstreip sumple containing exactly two ?'s and two l's G is 6 which are (3,3,1,1),(1,3,3,1), (1, 1, 3,3), (3,1,3,1) ; ( 3,1,1,3), (1,3,1,3) so the prot that a bootstrap sample. contains exactly too 3 s... and twol's 68 0.0234375 * ) 1,4= 4)

Hence 16 A dataset consists of 6 integers: 1, 2, 3, 4, 5, 6 let Pi & P2-be the probabilities of obtaining pattern (1,1,1,1,1,1) 8 (1,2,3,4,5,6) respectively. since bootstrap sampling is done with replacement and each indegen has equal prob of being included in the sample. P1 = (ab 4 pz = [ 16 The assertion pi= P2 is correct. A date & et consist of n consecutive integera : 1,2,3,..,6. for nas, integere are 1,2,3,4,5 The probability of obtaining a single number repeated times il. (5,5,5,5, si in a boodstup sample x 0:00 32. K 5 - Š x x x 5 5 5 5