by another medium day, with a probability of 0.6, and equally like to be followed by a good or bad day. A bad day has a 0.3 probability of being followed by a good day, 0.2 of being followed by a medium day, and a 0.5 probability of being followed by another bad day. Construct a Markov chain model to describe the way the fishing days run. Referring to problem 1 in Chapter 2 (the fishing problem – reproduced below), calculate what you need to answer the following questions: If the fishing is medium on Monday, what is the probability that it will be medium on Thursday? If yesterday’s fishing was bad, what is the expected number of days of good fishing over the new week (7 days)? What percentage of days over the long run are good fishing days? If the fishing is bad today, what is the expected time (in days) until it is good? If the fishing is bad today, how long (in expected number of days) will it remain
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Commercial fishermen in Alaska go into the Bering Sea to catch all they can of a particular species (salmon, herring, etc.) during a restricted season of a few weeks. The schools of fish move about in a way that is very difficult to predict, so the fishing in a particular spot might be excellent one day and terrible the next. The day-to-day records of catch size were used to discover that the probability of a good fishing day being followed by another good day is 0.5, by a medium day 0.3, and by a poor day 0.2. A medium day is most likely to be followed by another medium day, with a probability of 0.6, and equally like to be followed by a good or bad day. A bad day has a 0.3 probability of being followed by a good day, 0.2 of being followed by a medium day, and a 0.5 probability of being followed by another bad day. Construct a Markov chain model to describe the way the fishing days run.
Referring to problem 1 in Chapter 2 (the fishing problem – reproduced below), calculate what you need to answer the following questions:
- If the fishing is medium on Monday, what is the probability that it will be medium on Thursday?
- If yesterday’s fishing was bad, what is the expected number of days of good fishing over the new week (7 days)?
- What percentage of days over the long run are good fishing days?
- If the fishing is bad today, what is the expected time (in days) until it is good?
- If the fishing is bad today, how long (in expected number of days) will it remain bad before it gets better?
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