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Chapter 9: Q. 9.5 (page 412)

Consider Example 2a. If there is a 50–50 chance of rain today, compute the probability that it will rain 3 days from now if α = .7 and β = .3.

Short Answer

Expert verified

The probability that it will rain 3day from now is 12.

Step by step solution

01

Given Information  

We have given that there is 50–50 chance of rain today.

We need to find the probability that it will rain three days from now.

02

Simplify

Given a transition matrix

P=0.70.30.30.7

and the beginning distribution ( the distribution of X0) is

x0=0.50.5

To find the distribution of X3we have

localid="1648052534806" role="math" x3=P3x0=0.70.30.30.73.0.50.5

Now,

P3=0.5320.4680.4680.532

That is

localid="1648051526652" x3=0.50.5

So, that means there is the probability of 12that it will rain on the third day.

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