Statistics - MathematicalStatistics

Question 1: The green represents success, red failure, what is the probability of reaching the success node starting at node 1?

0 1/2 1/4 1

Question 2: What is the probability of reaching the success node starting at node 2?

1 1/4 1/2 0

Question 3: What is the probability of reaching the success node starting at node 0?

1 0 1/4 1/2

Question 4: Consider the same situation but with n nodes pictured here, what is the probability of reaching the success node from node n?

1/2 0 1/4 1

Question 5: What is the probability of reaching the success node from node 0 in the new n walk?

1/4 0 1 1/2

Question 6: What is the probability of reaching the success node from node j? (Hint: use recursion)

1 0 j/n 1-(j/n)

Question 7: How many steps will it take to finish the walk starting from node j?

$j$ j(n-j) n-j n(n-j)

Question 8: What is the expected number of steps to reach the success node from node j in 1 attempt?

$\frac{j(n-j)}{2}$ undefined 0 j(n-j)

Question 9: Is the expected number of steps to succeed or fail the sum of the expectation to fail, and succeed?

Yes, it is the sum of the expectations Only if the probabilities are 1 No, it is not the sum of the expectations Only if the probabilities are 0

Question 10: Explain the previous response

The expectation of steps is the sum of the 2 because they are the only 2 end nodes The expectation is only the sum when they have high probability The expectation is only the sum when they have low probability The expectation of steps has no information about which node it reaches

Quiz Questions