Register to reply

Probability question: random variables

by jezse
Tags: probability, random, variables
Share this thread:
May5-04, 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 mean-squared error (MMSE) estimate of U based on Y1 and Y2:
(b) Compute the resulting minimum mean-squared error.

Thank you.
Phys.Org News Partner Science news on
Sapphire talk enlivens guesswork over iPhone 6
Geneticists offer clues to better rice, tomato crops
UConn makes 3-D copies of antique instrument parts
May5-04, 07:09 PM
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,099
So what have you tried?

Register to reply

Related Discussions
A Probability Problem Involving 6 Random Variables Calculus & Beyond Homework 1
Probability of continuous random variables Calculus & Beyond Homework 5
Probability random variables Calculus & Beyond Homework 3
Probability inequality for the sum of independent normal random variables Set Theory, Logic, Probability, Statistics 3
Probability distribution of function of continuous random variables Set Theory, Logic, Probability, Statistics 1