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Probability question: random variables 
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#1
May504, 05:43 PM

P: 5

I have two questions.. any insight into either of them is appreciated.
1) A fair coin is tossed repeatedly; the sequence of outcomes is recorded. Let Y be the random time of the first appearance of HT (a tail immediately following a head). (a) Find P(Y = 4): (b) Find E[Y] (the expected time to wait for the first HT). (c) Find the expected length of the interval between successive appearances of HT. (d) Same as (c) for TT. 2) U is a random variable having mean 2 and variance 5. Two noisy measurements of U are taken: Y1 = U + Z1 Y2 = U + Z2: where Z1; Z2; U are assumed pairwise uncorrelated, and where E[Z1] = E[Z2] = 0; Var(Z1) = 1; Var(Z2) = 2: (a) Determine the linear meansquared error (MMSE) estimate of U based on Y1 and Y2: (b) Compute the resulting minimum meansquared error. Thank you. 


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