For a Poisson distribution X, suppose I know the variance of X is 5. (1) By property of Poisson, what is mean of X. (2) Compute P(X≥3) (3) Does Poisson have the property of lack of memory? List at least one name of distribution with such property. please explain full with all the steps
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
For a Poisson distribution X, suppose I know the variance of X is 5.
(1) By property of Poisson, what is mean of X.
(2) Compute P(X≥3)
(3) Does Poisson have the property of lack of memory? List at least one name of distribution with such property.
please explain full with all the steps
Given information:
A random variable X following Poisson distribution with variance 5.
Therefore, and ------(1)
However, variance of the random variable following the Poisson distribution is:
-----(2)
Thus, from equation (1) and (2), X is a Poisson random variable with parameter, .
(1) If X is the Poisson random variable, the mean of X is the parameter of the random variable X.
That is,
Therefore, with this property the mean of X is equal to the parameter, .
(2) The probability mass function of the Poisson random variable is :
The probability that X is greater than 3 is computed as:
Therefore, .
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