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A fair 6-sided die is rolled repeatedly.
(a) Find the expected number of rolls needed to get a 1 followed right away by a 2. Hint: Start by conditioning on whether or not the first roll is a 1.
(b) Find the expected number of rolls needed to get two consecutive 1's.
(c) Let an be the expected number of rolls needed to get the same value n times in a row (i.e., to obtain a streak of n consecutive j's for some not-specified-in-advance value of j). Find a recursive formula for an+1 in terms of an. Hint: Divide the time until there are n+1 consecutive appearances of the same valueinto two pieces: the time until there are n consecutive appearances, and the rest.
(d) Find a simple, explicit formula for an for all n ≥ 1. What is a7 (numerically)?
The Milesians and Heraclitus interpreted experience as, Positivism states that our descriptions and explanations of phenomena must be anchored in sense experience.
What is the difference between the cause and manner of death?
creation of human life in the laboratory
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Does the information presented in the article affect you or people you know? Explain.
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one of the greatest historical impacts of the enlightenment was the way it informed the american french haitian and
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