Consider a Markov chain with state space S = {1, 2, 3, 4, 5, 6} and transition probability matrix P = [ 0 0.5 0 0.1 0.4 0]
[ 0 1 0 0 0 0 ]
[ 0.3 0 0.2 0.1 0 0.4]
[0 0.7 0 0 0.3 0 ]
[0 0 0 0 1 0]
[0 0 0 0 0 1 ]
(a) Compute Pˣ. (b) If the process starts in state 3, what are the probabilities that it will be absorbed in state 2, state 5, and state 6, respectively?
a)Pˣ = [tex]\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}[/tex] in matrix form, using eigen-values.
b)state 2 is 0.75; state 5 is 0 and ;state 6 is 0.25.
a)In order to calculate the value of Pˣ, follow the below-given steps:
Step 1: Compute the eigen-values of the matrix P.
Here, we get λ = 1, λ = 0.6, λ = 0.4, λ = 0.1, λ = 0, λ = 0.
Step 2: Compute the eigen-vectors corresponding to each eigenvalue of the matrix P.
Step 3: Compute the diagonal matrix D and the transition matrix T. [tex]\begin{matrix}1 & 0 & 0 & 0 & 0 & 0\end{matrix}0.6[/tex]
[tex]\begin{matrix}0.58 & 0.25 & 0.72 & 0 & 0 & 0\end{matrix}0.4.[/tex]
[tex]\begin{matrix}0.07 & 0 & 0.04 & 0.7 & 0 & 0\end{matrix}0.1.[/tex]
[tex]\begin{matrix}0.35 & 0.75 & 0.56 & 0 & 1 & 0\end{matrix}0.[/tex]
[tex]\begin{matrix}0 & 0 & 0 & 0.3 & 0 & 1\end{matrix}[/tex]
Pˣ = T . Dˣ . T⁻¹
We get the following matrix as a result.
Pˣ = [tex]\begin{bmatrix}0.1 & 0.5 & 0.04 & 0.28 & 0.03 & 0.05\\0 & 1 & 0 & 0 & 0 & 0\\0.22 & 0 & 0.33 & 0.17 & 0.1 & 0.19\\0.7 & 0 & 0.43 & 0.3 & 0 & 0.57\\0 & 0 & 0 & 0 & 1 & 0\\0 & 0 & 0 & 0 & 0 & 1\end{bmatrix}[/tex]
b)If the process starts in state 3,
the probability that it will be absorbed in state 2 is 0.75,
the probability that it will be absorbed in state 5 is 0, and
the probability that it will be absorbed in state 6 is 0.25.
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Let A and B be disjoint compact subspaces of a Hausdorff space X. Show that there exist disjoint open sets U and V, with A⊂U and B⊂V.
In Hausdorff-space "X", if A and B are disjoint "compact-subspaces", then there exist disjoint "open-sets" U and V such that A is contained in U and B is contained in V, because Hausdorff property ensures the existence of disjoint open neighborhoods for any two distinct points.
To prove existence of disjoint "open-sets" U and V with A⊂U and B⊂V, where A and B are "compact-subspaces" (disjoint) of "Hausdorff-space" X, we use the steps:
Step (1) : Since A and B are disjoint compact subspaces, we use the Hausdorff property to find open sets Uₐ and [tex]U_{b}[/tex] such that A⊂Uₐ and B⊂[tex]U_{b}[/tex], and Uₐ∩[tex]U_{b}[/tex] = ∅. This can be done for every pair of points in A and B, respectively, since X is Hausdorff.
Step (2) : Consider the set U = ⋃ Uₐ, where "union" is taken over all of Uₐ for each point in A. U is = union of "open-sets", hence open.
Step (3) : Consider the set V = ⋃ [tex]U_{b}[/tex], where union is taken over for all [tex]U_{b}[/tex] for "every-point" in B. V is also a union of open-sets and so, open.
Step (4) : We claim that U and V are disjoint. Suppose there exists a point x in U∩V. Then x must be in Uₐ for some point a in A and also in [tex]U_{b}[/tex] for some point b in B. Since A and B are disjoint, a and b are different points. However, this contradicts the fact that Uₐ and [tex]U_{b}[/tex] are disjoint open sets.
Therefore, U and V are disjoint open sets with A⊂U and B⊂V.
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How do you find the radius of a circle?
Answer:
Divide the diameter by two
example if the diameter is 25 you divide 25 by 2 to get 12.5 as your radius .
You are a researcher studying the lifespan of a certain species of bacteria. A preliminary sample of 35 bacteria reveals a sample mean of = 66 hours with a standard deviation of 8 = 6.2 hours You would like to estimate the mean lifespan for this species of bacteria to within a margin of error of 0.5 hours at a 98% level of confidence. What sample size should you gather to achieve a 0.5 hour margin of error? Round your answer up to the nearest whole number. n= bacteria
You should gather a sample of at least 29 bacteria to estimate the mean lifespan for this species of bacteria with a margin of error of 0.5 hours at a 98% level of confidence.
We are given a preliminary sample of 35 bacteria with a sample mean of 66 hours and a standard deviation of 6.2 hours. We need to calculate the sample size required to achieve the desired margin of error.
To calculate the sample size, we can use the formula:
n = (Z * σ / E)²
Where:
n is the required sample size
Z is the z-score corresponding to the desired confidence level (98% confidence corresponds to a z-score of 2.33)
σ is the standard deviation of the population
E is the desired margin of error
Plugging in the values, we have:
n = (2.33 * 6.2 / 0.5)²
Calculating the expression within parentheses:
2.33 * 6.2 / 0.5 ≈ 28.84
Rounding up to the nearest whole number, the required sample size is 29 bacteria.
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here is my question.
Answer:
the answer is 18
Step-by-step explanation:
9X6=54
54/3=18
Answer:
18
Step-by-step explanation:
The top of a tall building has four triangular faces that slope toward a single point. What shape best models the top
of the building?
А cube
c. triangular pyramid
B cone
Dsquare pyramid
Choose
Answer:
Option D, square pyramid
Step-by-step explanation:
The base of a square pyramid is a square of side of length "A"
and the height of the pyramid is "h"
From the four sides of base of pyramid, four surfaces arises that are slanting and meet at a point at the top at height "h"
Hence, option D is correct
please and this quickly and no links please
Answer:
11 months
Step-by-step explanation:
Since he has already read 14 books subtract them from the 80 books. you'll end up with 66. then diviid by 6 and you'll get 11 months
Sue is 15 years older than Mike. in 5 years mikes’s age will be ½ sue’s age. What is the present age of each?
Show work!!!!
Answer:
5
Step-by-step explanation:
Sue in 5 years would 20, meaning Mike would be 10. Subtract 5 from Mike to get their current age.
Answer:
Mike= 10 years old
Sue= 25 years old
Step-by-step explanation:
Let the present age of Sue be s years old, while that of Mike be m years old.
Present
s= m +15 -----(1)
In 5 years
Sue's age= s +5
Mike's age= m +5
Given that Mike would be ½ of Sue's age in 5 years,
m +5= ½(s +5)
Multiply both sides by 2:
2(m +5)= s +5
Expand:
2m +10= s +5
2m +10 -5= s
s= 2m +5 -----(2)
Substitute (1) into (2):
m +15= 2m +5
2m -m= 15 -5
m= 10
Substitute m= 10 into (1):
s= 10 +15
s= 25
Thus, the present age of Mike is 10 years old and the present age of Sue is 25 years old.
Suppose the random variables X and Y have the following joint PDF: fxy(x, y) = cxy ,0 < x < b < 1 Determine the value of c.
The random variables X and Y have the value of c is 2/b².
Considering that the joint PDF of X and Y as fxy(x, y) = cxy ,0 < x < b < 1. Integrating the given PDF over its domain is necessary in order to determine the value of c. To find the worth of c, we utilize the accompanying integral:∫∫fxy(x, y)dxdy = 1,where the mix is done over the whole area of x and y. Therefore, cxy dxdy = 1. (1) For x, the integration limits are (0 to b) and for y, they are (0 to 1).
Therefore, by substituting these limits into equation (1), we obtain: 01 0b cxy dxdy = 1 c * [x2/2]0r1[y2/2]0rb = 1 c = 2 / b2 The value of c is therefore 2/b².
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What is the value of f(x) = 4x -9
Answer:
i believe its ()=4−9
Step-by-step explanation:
Answer:
f=4x-9
Step-by-step explanation:
f(x) = 4x-9
f(x)= 4x-9
x x
f=4x-9
Select the expression that is equivalent to (m2-16)
A
(m-4)2
B
(m+4)(m-4)
C
(m2+8m+16)
D
(m2-8m+16)
PLEASE HELP I AM BEING TIMED I NEED THE RIGHT ANSWER AND A EXPLAINTION PLEASE I WILL HIVE YOU THE CROWN
Answer:
B
Step-by-step explanation:
Dependent values would be the numbers on the y axis
def:This is what we call the money you get back when you pay for something.
term:
Answer:
Change
Step-by-step explanation:
I call what I get back in return, change. The money we get back if you pay extra for something you buy.
Hope this helps!
Instructions: Write the equation of the line in Slope-Intercept Form given the information below.
Slope =
-7/4
Y-Intercept = 5
Slope-Intercept Form:
Answer:-8
Step-by-step explanation:
Answer:
y = -7/4x + 5
Step-by-step explanation:
y = mx + b
y = -7/4x + 5
A sprinkler waters a circular area. The sprinkler sprays 30 gallons of water per minute.
Select as few quadrants as possible that would allow you to create a graph of the total number of gallons of water,
y, sprayed by the sprinkler after x minutes.
Quadrant 1
Quadrant 2
Quadrant 3
Quadrant 4
Answer:
Quadrant 1
Step-by-step explanation:
The number of gallons of water sprayed after x minutes would never be negative, nor would time be negative, so the first quadrant would be all that you need
Leo flips a paper cup 50 times and records how the cup landed each time. The table below shows the results.
RESULTS OF FLIPPING PAPER CUP
Outcome Right-side UP Upside Down On its Side
Frequency
10
18
22
Based on the results, how many times can he expect the cup to land on its side if it is flipped 1,000 times?
333
440
550
786
N
Previous
Answer:
440
Step-by-step explanation:
i did the test already
The rent for an apartment was $6,600 per year in 2012. If the rent increased at a rate of 4% each year thereafter, use an exponential equation to find the rent for the apartment in 2021
Answer:
$9,393.78
Step-by-step explanation:
Using the equation:
A = P(1+r)^t
Where,
A = final amount
P = initial amount = $6,600
r = rate of increase = 4% = 0.04
t = time in years = 9 years (2012-2021)
A = 6,600(1 + 0.04)^9
= 6,600(1.04)^9
= 6,600(1.4233)
= 9,393.78
A = $9,393.78
Joseph's front porch is rectangular. The length is 8 feet more than the width. The
perimeter of the porch is 52 feet. What is the width of the porch?
A. 9 feet
B. 14 feet
C. 17 feet
D. 22 feet
How many solutions does the system of linear equations have? Use the drop-down menus to explain your answer.
y = 3/4x + 12
y = 4/3x
The system of linear equations will have
Choose...
no solution
exactly one solution
infanite many solutions
because the slopes of the equations are
Choose...
the same
different
, so the lines will
Choose...
not intersect at all
intercect at one point
both be the same line
Answer:
There is one equation, the slopes are different so they will intersect at one point
Step-by-step explanation:
HURRY PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
option 3
Step-by-step explanation:
Answer:
wouldn't it be one, someone lmk if I'm right
Step-by-step explanation:
48 is half of 96 and the ratio says there are less trucks. 36 is the closest to 48 but still less than it.
El auto que se va a comprar Pablo necesita que un cambio de aceite cada 60.000km y de neumáticos cada 90.000km. ¿En cuántos kilómetros coincidirá por primera vez el cambio de aceite y de neumáticos?
Answer:
El cambio de aceite y de neumáticos coincidirá por primera vez en 180.000 km.
Step-by-step explanation:
Como tenemos que encontrar cuándo se realizarán los dos cambios al mismo tiempo por primera vez, esto significa que tenemos que encontrar el mínimo común múltiplo de los dos números dado que este es el múltiplo más pequeño que tienen en común esos números y es donde coinciden por primera vez. Para encontrar el mínimo común múltiplo, puedes escribir los múltiplos de cada número y encontrar los que son comunes y seleccionar el más pequeño.
Múltiplos de 60.000= 60.000, 120.000, 180.000, 240.000, 300.000, 360.000, 420.000
Múltiplos de 90.000= 90.000, 180.000, 270.000, 360.000, 450.000, 540.000, 630.000
De acuerdo a esto, el mínimo común múltiplo es 180.000 dado que es el múltiplo más pequeño en el que coinciden y la respuesta es que el cambio de aceite y de neumáticos coincidirá por primera vez en 180.000 km.
f left parenthesis x right parenthesis equals 3 over 4 x squared .
Answer:
Step-by-step explanation: try your best
In a standard deck of cards, what is the probability of drawing a face card followed by drawing a non-face card? Answer choices are in the form of a percentage, rounded to the nearest whole number.
a.) 45%
b.)27%
c.)4%
d.)18%
Reason:
The face cards are Jack, Queen, and King. There are 3 face cards per suit, and 4 suits, giving 3*4 = 12 face cards and 52-12 = 40 non-face cards in a standard deck.
12/52 = probability of getting a face card on 1st draw40/51 = probability of getting a non-face card on 2nd drawThe 52 dropped to 51 because we are not putting the 1st card back.
Multiply out those fractions:
(12/52)*(40/51) = 0.180995 approximately.
Move the decimal point two spots to the right to convert to a percentage.
0.180995 becomes 18.0995% and rounds to 18%
In a standard deck of cards, there are 12 face cards (4 kings, 4 queens, and 4 jacks) out of a total of 52 cards. The probability of drawing a face card followed by drawing a non-face card from a standard deck of cards is 18%.
To calculate the probability, we first determine the probability of drawing a face card on the first draw, which is 12/52 or 3/13. After drawing a face card, there are 51 cards remaining in the deck, of which 40 are non-face cards. Therefore, the probability of drawing a non-face card on the second draw, given that a face card was drawn on the first draw, is 40/51.
To find the overall probability of drawing a face card followed by a non-face card, we multiply the probabilities of the individual events. So the probability is (3/13) * (40/51) = 120/663, which is approximately 0.181 or 18%. Rounded to the nearest whole number, the probability is 18%.
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How is 0.00400068 expressed in standard scientific notation?
Answer:
4.00068 × [tex]10^{-3}[/tex]
If Lin runs 21 laps at the same rate, how long does it take her?
minutes
What is 14 + 6 =
+11
Since, 14 + 6 = 20
Therefore, 14 + 6 = 9 + 11
dont forget to like and mark me
Answer:
31
Step-by-step explanation:
The maximum weight of a shipping container is 125 pounds. What is the maximum weight in kilograms?
a. 56.7 kg
b. 62.5 kg
c. 75 kg
d. 100 kg
The maximum weight in kilograms is approximately 56.7 kg. Hence, the correct option is (a) 56.7 kg.
The maximum weight of a shipping container is 125 pounds.
We need to find out what is the maximum weight in kilograms.
Step 1: Find out 1 pound weight in kilograms We know that 1 pound = 0.45359237 kilograms (we already know that)
Step 2: Convert the maximum weight in pounds to kilograms
Maximum weight in pounds = 125 Maximum weight in kilograms
= 125 x 0.45359237
= 56.69904625≈ 56.7 kg
Therefore, the maximum weight in kilograms is approximately 56.7 kg.
Hence, the correct option is (a) 56.7 kg.
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Simplify the expression 7 − 1x −1(−5x) − 10 + 4x
Answer: 3x-1(-5x)-3
Step-by-step explanation:
−3-x-1(-5x)+4x
-3+3x-1(-5x)
3x-1(-5x)-3
Caleb has a guaranteed minimum salary of $1,200 per month, or 5.5% of his total monthly sales (as commission), whichever is higher. Last month, his total sales were $45,000. What was his gross pay?
Answer: $1,200 + 5.5% + $45,000= 46200.055 or 46200
Step-by-step explanation: All you have to do is just add because if you read the text it has a key word total.
Caleb has a guaranteed minimum salary of $1,200 per month, or 5.5% of his total monthly sales (as commission), whichever is higher. Last month, his total sales were $45,000. What was his gross pay?
What is the area of a regular hexagon with an apothem of 28m in length
Step-by-step explanation:
can you check again the question , seems like something is missing.