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Definition of distribution theory
Distribution theory, also known as a 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
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) P (0.02777) 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. Get instant help with your joint probability assignment from our experts now. Our statistics assignment helpers will provide you with precise and accurate solutions.
- Probability density function (PDF)
- Power series distribution
- Sampling distributions
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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