1. A bag contains 10 red, 12 green, and 8 yellow marbles. Assuming that all marbles are equally likely to be picked from the bag, what is the probability that the second marble is yellow, given that the first marble was yellow?

2. Given the following information, calculate the Predictive value positive and the Predictive value negative.

Prevalence =5%
Sensitivity =85%
Specificity =74%

3. Find a steady state distribution vector for the Markov chain with transition

[0.25 0.75]
P=
[0.2 0.8]

4. A couple has 8 foster children, including 3 girls and 5 boys. Two-thirds of the girls have brown eyes. What is the probabiliy that a randomly selected child is a brown-eyed girl?

5. The probability of moving from a state i to a state j is called the?

6. Given the following information, compute the PVP using Bayes' Theorem. Prevalence = 20% Sensitivity = 50% Specificity = 75%

Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.

See attached file for better format.
A particle moves on the states 1, 2, 3, and 4 according to a time-homogeneous Markov chain {Xn ; n ≥ 0 }
with initial distribution p(0) = ( .2, .8, 0, 0 ) and transition matrix : p = [■(.6&.4&0&0@.6&0&.4&0@0&.6&0&.4@0&0&.6&.4)]
a) Draw the state diagram of the chain.

Category: Statistics > Simple Regression
Subject: birth-death process
Details: Let a Markov chain have transition probabilities Pi,i+1 = 1/(i+1) and Pi,0 = i/(i+1) for i=0,1,2, . . . .
i) Is the chain positive recurrent? Or transient or null recurrent?
ii) Does a stationary distribution exist? If it does, what is it?
S

This problem involves the use of Matlab.
Step 1: Choose any Markov Chain with a 3x3 transition matrix that is irreducible and aperiodic. The reason it needs to be irreducible and aperiodic is because we are looking for a Markov Chain that converges. Calculate the stationary distribution of the Markov Chain by hand.
Ste

Please see attached file.
Consider the Markov chain with transition matrix (please see the attached file) where 0 <= p <= 1 and 0 <= q <= 1. Find an invariant distribution of this chain, For which values of p and q is the distribution unique? Given an initial distribution (please see the attached file), for which values of p

Markov chains. I am finding the continuous case a bit unintuitive. This problem concerns martingales and branching processes, but it is supposedly not hard. I just need a detailed solution to this problem, so that I can see what concepts are used to solve it.

Why is using Bayes' theorem important to help answer business-related questions? What does this theorem allow you to do that traditional statistics do not? What are some prerequisites for using Bayesian statistics?

Why is using Bayes' theorem important to help answer business-related questions? What does this theorem allow you to do that traditional statistics do not? What are some prerequisites for using Bayesian statistics?

1. Suppose that shocks occur according to a Poisson process with rate A> 0. Also suppose that each shock independently causes the system to fail with probability 0 < p < 1. Let N denote the number of shocks that it takes for the system to fail and let T denote the time of the failure.
(a) FindP{T>tNrrn}.
(b) FindP{NrrnT=t}.
(

Suppose that, in a particular city, airport A handles 50% of all airline traffic, and airports B and C handle 30% and 20%, respectively. The detection rates for weapons at the three airports are .9, .5, and .4, respectively. If a passenger at one of the airports is found to be carrying a weapon through the boarding gate, what is