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Discrete Distribution Homework Help

A discrete Distribution is a probability distribution which is distinguished by mass function of probability. So, the distribution of a random variable Z is considered to be discrete. Z will be considered a discrete variable if the following function comes out to be 1.
Σ_u Pr⁡( Z=u)= 1

Where, u should run through all the values of Z, a random variable like Z can be assumed to have only finite number of value. The above set is a topological set, a set is said to be topologically discrete when all its points are isolated. There are some random variables which have infinite sets on a real line. For example, a distribution of random nos. can be considered one example where there will be countable sets which are dense on real line. The most popular discrete distributions are the Bernoulli probability distribution, the binominal distribution, the Poisson distribution, the geometric distribution, and the negative binominal distribution. In some case user needs discrete uniform distribution, like for computer programs we need discrete uniform distribution to make choices between numbers. Below is the diagram of probability of mass function for a discrete distribution. It shows the probabilities of single nos. 1, 3, and 7. Now, if a set is not containing any of the above nos. will have a probability zero.

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