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Discrete Probability Distribution – If the probabilities are defined on a discrete random variable, one which can only take a discrete set of values, then the distribution is said to be a discrete probability distribution. For example, the event of rolling a die can be represented by a discrete random variable with the probability distribution being such that each event has a probability of
. - Continuous Probability Distribution – If the probabilities are defined on a continuous random variable, one which can take any value between two numbers, then the distribution is said to be a continuous probability distribution. For example, the temperature throughout a given day can be represented by a continuous random variable and the corresponding probability distribution is said to be continuous.
Uniform Probability Distribution –
The Uniform Distribution, also known as the Rectangular Distribution, is a type of Continuous Probability Distribution. It has a Continuous Random Variable
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Example 1 – The current (in mA) measured in a piece of copper wire is known to follow a uniform distribution over the interval [0, 25]. Find the formula for the probability density function
of the random variable representing the current. Calculate the mean, variance, and standard deviation of the distribution and find the cumulative distribution function . -
Solution – The first step is to find the probability density function. For a Uniform distribution,
, where are the upper and lower limit respectively. The cumulative distribution function is given as- There are three regions where the CDF can be defined,
References –
Probability Distribution – Wikipedia Uniform Probability Distribution – statelect.com
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