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### Question

1. Let {Xn}n≥0 be a discrete-time Markov chain on the state space S = {1,2,3} with transition matrix P =ï£« ï£­ 1/3 1/3 1/3 0 2/3 1/3 1/3 2/3 0 ï£¶ ï£¸.If the initial distribution is
P(X0 = 1) = P(X0 = 2) = P(X0 = 3) = 1/3, what is P(X3 ∈{2,3})? 2. Let Π be a homogeneous Poisson point process on the line, with intensity λ. Let r+ be the distance from the origin O to the closest point of Π on the positive axis and r− be the distance from O to the closest point of Π on the negative axis. Find the distribution functions of these random variables: i.e., ï¬nd P(r+ ≤ x) and P(r− ≤ x) for x ≥ 0. Find also the distribution function of the distance from O to the closest point of Π: i.e., ï¬nd P(min(r−,r+) ≤ x). 3. Let the continuous-time Markov process {X(t)}t≥0 on the state space S = {1,2,3,4} have the matrix of transition rates

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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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### MFA501 Mathematical Foundations of Artificial Intelligence

Question: Task: This assessment allowed you to show your understanding on how to choose the correct AI method to solve simple case studies. The Assessment has been designed to assess your ability in choosing and using the best AI methods to solve larger and more challenging problems. The AI me ...

Q

### Management

Interpret and analyse collected data. Evaluate data to theorise developments, draw conclusions and identify implications. Presented with correct grammar, spelling and appropriate academic referencing. ...

Q

...

Q

### 969G5 Algorithmic Data Science

Question: Scenario Imagine, you have a collection of d (d > 10) documents each containing at least w (w > 50) English words. For testing purposes, you may wish to construct or collect such a collection. A document can be represented as a bag-of-words, i.e., as the set of the words it contain ...

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