Register to reply

Probability question: random variables

by jezse
Tags: probability, random, variables
Share this thread:
jezse
#1
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 Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
Hurkyl
#2
May5-04, 07:09 PM
Emeritus
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,091
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