Probability 6

Probability 8

combination and probability

Probabilty

Can you please explain which answer is correct. I'm undecided on whether b or c is the correct answer. Thanks

Can you please explain which answer is correct. I'm undecided on whether a or b is the correct answer. Thanks

Can you please explain which answer is correct. I'm undecided on whether d or e is the correct answer. Thanks

data G12 2

Data management 1

If I have a discrete random process (✗n) n≥20 on two states where for each n, ✗, is independent of X-3, Xn-4, ... Xo when conditioned on Xn-1 and Xn-2, then a. This process is a Markov chain because the future is independent of the past conditioned on the present. b. This process is not a Markov chain but it can be turned into a Markov chain on 4 states. c. This process is a Markov chain because although it does not fit the exact definition, the way it differs is just a technicality. d. This process is not a Markov chain because it does not fit the mathematical definition and this definition is quite strict. e. This process is not a Markov chain but it can be turned into a Markov chain on 3 states.

Which of the following processes does not have the Markov property? a. The process (✗n) n≥0 of sampling a ball from an urn and noting its colour, if one samples without replacement. b. The process (Xn)n20 of sampling a ball from an urn and noting its colour, if one samples with replacement. c. The process (✗n)n≥0 defined by X = Y1 + ··· + Y2 for n ≥ 1, where for each n, Y equals one if a fair coin toss lands heads, and equals 0 otherwise. d. The process (Xn) n≥0 where X represents the outcome of rolling a fair 6-sided die. e. The process (X)n≥0 where X represents the outcome of rolling a fair 6-sided die for 0 ≤ n ≤ 5 and the outcome of throwing a fair coin for n> 6.

Two machines are running continuously, with their operating states described by two Markov chains. For each machine, the possible states are {1, 2, 3, 4, 5, 6}. The state of the first machine on day n is ✗r. The state of the second machine on day n is Yr. The transition matrices for (Xn)n20 and (Y)n20 are P and Q respectively where: 1/3 2/3 0 0 0 0 01 0 1/3 4/9 2/9 0 0 0 0 000 2/3 1/3 0 0 0 0 0 1/3 0 1/3 1/3 0 0 0 0 1/2 1/2 P = ; Q: = 0 0 0 1/3 4/9 2/9 0 0 0 0 2/3 1/3 2/3 0 0 0 1/3 0 1 0 0 0 0 0 2/3 0 0 00 1/3 1 0 0 00 0 Let w = (1/4 1/4 1/6 1/12 5/36 1/9). Then a. the vector w is a limiting distribution for (✗n)n≥0 and (Yn)n≥0; O b. the vector w is a limiting distribution for (✗n) n≥0 but not (Yn)n>0; ○しろまる c. ○しろまる d. the vector w is a limiting distribution for neither (✗n) n≥0 nor (Yn)n≥0; the vector w is a limiting distribution for (Yn) n≥0 but not (✗n)n≥0;