(1) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probat (i) If volume is low this week then it will be high next week with a probability of O0.3. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. P = (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now (3) What is the probability that volume will be high for three consecutive weeks?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
Solve bout the volume of securities sold by a brokerage firm, using the following data:
![**Markov Process Problem Set**
In this exercise, we are examining a Markov process involving weekly volume states. The states are defined as follows:
- **State 1**: High Volume
- **State 2**: Low Volume
Given the following transition probabilities:
(i) If the volume is high this week, next week it will be high with a probability of 0.9 and low with a probability of 0.1.
(ii) If the volume is low this week, next week it will be high with a probability of 0.3 and low with a probability of 0.7.
**Tasks:**
1. **Transition Matrix Construction**: Construct the transition matrix \( P \) for this Markov process.
\[
P = \begin{bmatrix}
\text{[Probability from state 1 to state 1]} & \text{[Probability from state 1 to state 2]} \\
\text{[Probability from state 2 to state 1]} & \text{[Probability from state 2 to state 2]}
\end{bmatrix} = \begin{bmatrix}
0.9 & 0.1 \\
0.3 & 0.7
\end{bmatrix}
\]
2. **Two-Week Probability**: If the volume this week is high, find the probability that the volume will be high two weeks from now.
3. **Three Consecutive Weeks Probability**: What is the probability that the volume will be high for three consecutive weeks?
These questions engage your understanding of Markov processes and involve calculations with transition matrices to predict state changes over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4da1f4c8-4970-49e9-beef-0939f39f632e%2Fbdfd0033-5272-4715-ab7e-29930f9d8a69%2Fhf5ssqr_processed.png&w=3840&q=75)
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