Distribution Theory Assignment Help
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Definition of distribution theory
Distribution theory, also known as probability distribution is a mathematical function used to determine possible outcomes of events. It involves carrying out an experiment to explain a random phenomenon about the probability of an event occurring. For example, when you toss a coin, the chances of it landing on the head or tail is both 0.5.
Popular concepts in distribution theory
- Joint Probability
In joint probability, there is a chance of more than one event occurring at the same time. For two events A and B, the joint probability can be expressed mathematically in the following way: P (A, B)
To calculate joint probability, multiply the probability of event A by that of B. This can be expressed as P (A) x P (B)
Calculate the probability that the number 5 will occur twice when two dices are rolled at the same time.
Each die has six possible outcomes. However, the probability of the number 5 occurring is 1/6 for each dice: We can use joint probability to calculate this as shown below:
Take the first dice as event A and the second one as B.
The probability will be P (A) = 0.1666 and P (B) = 0.1666
The formula for joint probability is P (A, B)
So, P (0.1666 x 0.1666)
This means that the joint probability of the number 5 occurring when both dice are rolled at the same time is 0.02777.
Why joint probability is important
Joint probability can be used when two or more observable phenomena occur simultaneously. A good example is the decline in the Dow Jones Industrial Average and the substantial loss in the value of the dollar. However, the only disadvantage of this method is it cannot be used to determine how the occurrence of one event influences the other. One would have to calculate conditional probability to know this.
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- Probability density function (PDF)
Probability density function is calculated to determine the probabilities associated with a continuous random variable. A PDF graph curves above the horizontal axis. The graph defines the total area between the axis of 1 and itself. Many students struggle with assignments on this topic. If you are one of them, then we recommend that you hire our probability theory homework helpers.
- Power series distribution
These are discrete distributions constructed from power series on a subset of N. Power series distributions are essential because most discrete distributions are power series distributions. We are available round the clock to assist you with academic tasks related to power series distributions. Submit your assignment to us and wait for our experts to help you reap excellent grades.
- Sampling distributions
This is a probability distribution of a statistic. It is obtained by drawing a large number of samples from a specific population. For a given population, a sampling distribution is the distribution of frequencies of different outcomes that could possibly occur for a statistic. For example, a researcher that wants to compare the weight of all babies born in Europe from 2010 to 2020, to those born in North America within the same period cannot possibly draw the data of the entire population. Since more than a million childbirths may have happened over the ten-year time frame, the researcher may choose to use the weight of, say, 100 babies in each of the continents to make a decision. The sample is the weight of the 200 babies used, while the average weight calculated is the sample mean.
Suppose the researcher, instead of collecting just one sample of 100 newborn weights from each continent, decided to take repeated random samples to calculate the sample mean. He collects data of 100 birth weights from each of the countries in North America and Europe. The sampling distribution mean will be the average weight computed for each sample set. Apart from the mean, other statistics such as variance, standard deviation, proportion, and range can also be calculated from sample data.
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- Order statistics
The system of placing sample values in ascending order is known as order statistics. This concept handles the functions and the applications of these ordered values. For example, if we have three weights: x1 = 22 kg, x2 =44 kg and x3 = 12kg
To get the order statistics (Yn), the items are placed in ascending order:
Y1 = 12kg
Y2 = 22Kg
Y3 = 44kg
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