Answer:
6
Step-by-step explanation:
S = Spanish book
M = Math book
H = History book
These are the different ways in which he can organize the book on his bookshelf.
SMH
SHM
MSH
MHS
HSM
HMS
There are 6 ways.
There are 2 factors in this expression
Answer:
Probability distribution vector =
Step-By-Step Explanation
If
is the transition matrix for a Markov chain with two states.
be the initial state vector for the population.
In the long run, the probability distribution vector Xm approaches the probability distribution vector
.
This is called the steady-state (or limiting,) distribution vector.
Answer:


Step-by-step explanation:
Given



Required
Find P(A) and P(B)
We have that:
--- (1)
and
--- (2)
The equations become:
--- (1)

Collect like terms


Make P(A) the subject

--- (2)


Substitute: 
![[0.770 - P(B)] * P(B) = 0.144](https://tex.z-dn.net/?f=%5B0.770%20-%20P%28B%29%5D%20%2A%20P%28B%29%20%3D%200.144)
Open bracket

Represent P(B) with x

Rewrite as:

Expand

Factorize:
![x[x - 0.45] - 0.32[x - 0.45]= 0](https://tex.z-dn.net/?f=x%5Bx%20-%200.45%5D%20-%200.32%5Bx%20-%200.45%5D%3D%200)
Factor out x - 0.45
![[x - 0.32][x - 0.45]= 0](https://tex.z-dn.net/?f=%5Bx%20-%200.32%5D%5Bx%20-%200.45%5D%3D%200)
Split

Solve for x

Recall that:

So, we have:

Recall that:

So, we have:


Since:

Then:

