题目内容

(c) Let Yₖ denote the result of the kᵗʰ roll. Let X₁=Y₁, and for k≥2, let Xₖ=Yₖ+Yₖ₋₁. Does the sequence X₁,X₂,… satisfy the Markov property?

A. Yes
B. No

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(b) Let Xₖ denote the number of 6's obtained in the first k rolls, up to a maximum of ten. (That is, if ten or more 6's are obtained in the first k rolls, then Xₖ=10.) Does the sequence X₁,X₂,… satisfy the Markov property?

A. Yes
B. No

PROBLEM 3: CHECKING THE MARKOV PROPERTY For each one of the following definitions of the state Xₖ at time k (for k=1,2,…), determine whether the Markov property is satisfied by the sequence X₁,X₂,….A fair six-sided die (with sides labelled 1,2,…,6) is rolled repeatedly and independently.(a) Let Xₖ denote the largest number obtained in the first k rolls. Does the sequence X₁,X₂,… satisfy the Markov property?

A. Yes
B. No

p₀₀=______

For i∈{1,2,3,4},pᵢᵢ=______