Consider the following Markov chain:
0
1
2
3
0
0.3
0.5
0
0.2
1
0.5...
Consider the following Markov chain:
0
1
2
3
0
0.3
0.5
0
0.2
1
0.5
0.2
0.2
0.1
2
0.2
0.3
0.4
0.1
3
0.1
0.2
0.4
0.3
What is the probability that the first passage time
from 2 to 1 is 3?
What is the expected first passage time from 2 to
1?
What is the expected first passage time from 2 to 2
(recurrence time for 2)? What is the relation between this
expectation and the steady-state probability of being at state
2?
Mg standard
Absorbance
%RSD
0.5
0.09533
0.3
1
0.1209
0.2
2
0.17304
0.3
5
0.28137
0.2
10
0.56901
0.5
20
0.87153
0.3
5 mL Unk
0.14296
0.2
[1] Make a calibration curve using the absorbances for the
samples from 0.5 – 20 ppm. Include the intercept (0,0) as a data
point.
[2] Is the calibration linear, i.e., does the analysis follow
Beer’s law? To discuss linearity, examine both the trend of the
data relative to the least squares line and...
x −4 −3 −2 −1 0 P(X=x) 0.2 0.1 0.3 0.2 0.2
Step 1 of 5: Find the expected value E(X). Round your answer to
one decimal place.
Step 2 of 5:
Find the variance. Round your answer to one decimal place.
Step 3 of 5:
Find the standard deviation. Round your answer to one decimal
place.
Step 4 of 5:
Find the value of P(X>−1)P(X>−1). Round your answer to one
decimal place.
Step 5 of 5:
Find the value...
Consider a Markov chain {Xn|n ≥ 0} with state space S = {0, 1, ·
· · } and transition matrix (pij ) given by pij = 1 2 if j = i − 1
1 2 if j = i + 1, i ≥ 1, and p00 = p01 = 1 2 . Find P{X0 ≤ X1 ≤ · ·
· ≤ Xn|X0 = i}, i ≥ 0
. Q2. Consider the Markov chain given in Q1. Find P{X1,...
The following is the transition probability matrix of a Markov
chain with states 1, 2, 3, 4 P
0
1
2
3
0
.4
.3
.2
.1
1
.2
.2
.2
.4
2
.25
.25
.5
0
3
.2
.1
.4
.3
If Xnot = 1
(a) find the probability that state 3 is entered before state
4;
(b) find the mean number of transitions until either state 3 or
state 4 is entered.
Let {Xn|n ≥ 0} is a Markov chain with state space S = {0, 1, 2,
3}, and transition probability matrix (pij ) given by 2 3 1 3
0 0 1 3 2 3 0 0 0 1 4 1 4 1 2 0 0 1 2 1 2 Determine all
recurrent states. Q3. Let {Xn|n ≥ 0} is a Markov chain with state
space S = {0, 1, 2} and transition probability matrix (pij...
x
0
1
2
3
4
P(X)
0.45
0.3
0.2
0.04
0.01
(a) Find and interpret the expected value of X
(b)Find the variance of X
(c)Find the probability that a person has 1 sibling given that
they have less than 3 siblings.
(d)Find the probability that a person has at least 1 sibling OR
less than 2 siblings
Consider the following data:
x
-4
-3
-2
-1
0
P(X=x)
0.2
0.1
0.2
0.1
0.4
Step 2 of 5 : Find the variance. Round your answer to one
decimal place.
Step 3 of 5 : Find the standard deviation. Round your answer to
one decimal place.
Correlations: -0.9, -0.5, -0.2, 0, 0.2, 0.5, and 0.9. For each,
give the fraction of the variation in Y that is explained by the
least- squares regression of Y on X. Summarize what you have found
from performing these calculations.
Xn is a Markov Chain with state-space
E = {0, 1, 2}, and transition matrix
0.4 0.2 0.4
P = 0.6 0.3 0.1
0.5 0.3 0.2
And initial probability vector a = [0.2, 0.3,
0.5]
For the Markov Chain with state-space, initial vector, and
transition matrix discuss how we would calculate the follow;
explain in words how to calculate the question below.
a) P(X1 = 0, X2
= 0, X3 = 1, X4 =
2|X0 = 2)
b) P(X2 =...