What Prob distribution is
Probability distribution is a mathematical function that describes the probabilities of various outcomes in a given situation or experiment. It is a useful tool in making decisions and predicting outcomes, as it allows us to assign probabilities to events.
Steps for Probability Distribution:
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Identify the possible outcomes of the experiment. This will depend on the nature of the experiment, but a few examples of outcomes could be the number of heads when flipping a coin, the number of red cards in a deck of cards, or the length of a customer’s visit to a store.
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Assign a probability to each outcome. This can be done by taking the number of possible outcomes and dividing it by the total number of possible outcomes. For example, if there are four possible outcomes in an experiment, and each outcome has an equal chance of occurring, then the probability of each outcome would be 0.25.
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Calculate the probability of each outcome. This is done by multiplying the probability of each outcome by the number of times it can occur. For example, if there are four possible outcomes in an experiment, and each outcome has a probability of 0.25, then the probability of one of those outcomes occurring would be 0.25 x 4 = 1.
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Plot the probability distribution. This can be done on a graph, where the x-axis is the outcomes and the y-axis is the probability of each outcome. This will allow you to visualize the probability of each outcome occurring.
Examples
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The probability distribution of a six-sided die roll can be modeled by a discrete uniform distribution.
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The probability distribution of a coin flip can be modeled by a Bernoulli distribution.
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The probability distribution of a normal random variable can be modeled by a normal distribution.
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The probability distribution of blood pressure measurements in a population can be modeled by a gamma distribution.
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The probability distribution of waiting times between customer arrivals at a store can be modeled by an exponential distribution.