I have two questions.. any insight into either of them is appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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 mean-squared error (MMSE) estimate of U based on Y1 and Y2:

(b) Compute the resulting minimum mean-squared error.

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Probability question: random variables

**Physics Forums | Science Articles, Homework Help, Discussion**