Thanks in advance for the help
2 answers:
For this case we must find the graphical solution of the following system of equations:
In the attached image it is observed that the lines are parallel, they are intercepted in all the points. In addition, it is observed that if we divide the second equation by 5 we obtain:, if we now multiply by 3 we obtain:
. Being shown that the lines are equal, therefore, the system has more than one solution.
ANswer:
Option B
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Answer:
the proportion of days that are Sunny is 0.2
Step-by-step explanation:
Given the data in the question;
Using markov chain;
3 states; Sunny(1), Cloudy(2) and Rainy(3)
Now, based on given conditions, the transition matrix can be obtained in the following way;
so let the proportion of sunny, cloudy and rainy days be S, C and R respectively.
such that, from column 1
S = 0.25C + 0.25R -------------let this be equation 1
from column 2
0.5C = 0.5S + 0.25R
divided through by 0.5
C = S + 0.5R ---------------------- let this be equation 2
now putting equation 2 into equation;
S = 0.25(S + 0.5R) + 0.25R
S = 0.25S + 0.125R + 0.25R
S - 0.25S = 0.375R
0.75S = 0.375R
S = 0.375R / 0.75
S = 0.5R
Therefore,
from equation 2; C = S + 0.5R
input S = 0.5R
C = 0.5R + 0.5R
C = R
Now, we know that, the sum of the three proportion should be equal to one;
so
S + C + R = 1
since C = R and S = 0.5R
we substitute
0.5R + R + R = 1
2.5R = 1
R = 1/2.5
R = 0.4
Hence, the proportion of days that are Rainy is 0.4
C = R
C = 0.4
Hence, the proportion of days that are Cloudy is 0.4
S = 0.5R
S = 0.5(0.4)
S = 0.2
Hence, the proportion of days that are Sunny is 0.2