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Suppose we play a game where we start with c dollars. On each play of the game you either double or halve your money, with equal probability. What is your expected fortune after n trials?1. 2. Show that V(X) = 0 if and only if there is a constant c such that P (X = c)= 1.
3. Let X1,..., Xn ∼ Uniform(0, 1) and let Yn = max{X1,..., Xn}. Find E(Yn).
4. A particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump the probability is p that the particle will jump one unit to the left and the probability is 1-p that the particle will jump one unit to the right. Let Xn be the position of the particle after n units. Find E(Xn) and V(Xn). (This is known as a random walk.)
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alex sells exciting world of statistics videos over the phone to earn some extra cash during the economic crsis. only
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Find an unbiased estimator of mp(1 - p)/n. Find the optimal estimator using the Rao-Blackwell Theorem.
for the demand equation below x represents the quantity demanded in units of 1000 and p is the unit price in dollars.
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