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How can you prove that a random variable follows the Poisson distribution?
Wiki User
∙ 16y ago
You could draw a Probability Plot: "The probability plot ... is a graphical technique for assessing whether or not a data set follows a given distribution such as the normal or Weibull. "The data are plotted against a theoretical distribution in such a way that the points should form approximately a straight line. Departures from this straight line indicate departures from the specified distribution." Source: Online Engineering Statistics Handbook http://www.itl.nist.gov/div898/handbook/eda/section3/probplot.htm
Wiki User
∙ 16y ago
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What is the Test for normal distribution?
Normal Distribution is a key to Statistics. It is a limiting case of Binomial and Poisson distribution also. Central limit theorem converts random variable to normal random variable. Also central limit theorem tells us whether data items from a sample space lies in an interval at 1%, 5%, 10% siginificane level.
How do you get the median of a continuous random variable?
You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
What is meant by probability distribution?
I will give first the non-mathematical definition as given by Triola in Elementary Statistics: A random variable is a variable typicaly represented by x that has a a single numerical value, determined by chance for each outcome of a procedure. A probability distribution is a graph, table or formula that gives the probabability for each value of the random variable. A mathematical definition given by DeGroot in "Probability and Statistics" A real valued function that is defined in space S is called a random variable. For each random variable X and each set A of real numbers, we could calculate the probabilities. The collection of all of these probabilities is the distribution of X. Triola gets accross the idea of a collection as a table, graph or formula. Further to the definition is the types of distributions- discrete or continuous. Some well know distribution are the normal distribution, exponential, binomial, uniform, triangular and Poisson.
What will be the sampling distribution of the mean for a sample size of one?
It will be the same as the distribution of the random variable itself.
What are the 2 conditions that determine a probability distribution?
The value of the distribution for any value of the random variable must be in the range [0, 1]. The sum (or integral) of the probability distribution function over all possible values of the random variable must be 1.
Can the Poisson distribution be a continuous random variable or a discrete random variable?
True
If the outcomes of a random variable follow a Poisson distribution then their?
means equal the standard deviation
What is the probability that a Poisson random variable x is equal to 5...?
It depends on the parameter - the mean of the distribution.
What is the Probability density function of Poisson distribution?
If a random variable X has a Poisson distribution with parameter l, then the probability that X takes the value x isPr(X = x) = lx*e-l/x! for x = 0, 1, 2, 3, ...
What is the distribution of the sum of squared Poisson random variables?
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What is the Test for normal distribution?
Normal Distribution is a key to Statistics. It is a limiting case of Binomial and Poisson distribution also. Central limit theorem converts random variable to normal random variable. Also central limit theorem tells us whether data items from a sample space lies in an interval at 1%, 5%, 10% siginificane level.
Poisson distribution the mean and standard deviation?
The Poisson distribution is a discrete distribution, with random variable k, related to the number events. The discrete probability function (probability mass function) is given as: f(k; L) where L (lambda) is the mean and square root of lambda is the standard deviation, as given in the link below: http://en.wikipedia.org/wiki/Poisson_distribution
How do you compute the probability distribution of a function of two Poisson random variables?
we compute it by using their differences
How do you get the median of a continuous random variable?
You integrate the probability distribution function to get the cumulative distribution function (cdf). Then find the value of the random variable for which cdf = 0.5.
Can the variance of a normally distributed random variable be negative?
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.
What is meant by probability distribution?
I will give first the non-mathematical definition as given by Triola in Elementary Statistics: A random variable is a variable typicaly represented by x that has a a single numerical value, determined by chance for each outcome of a procedure. A probability distribution is a graph, table or formula that gives the probabability for each value of the random variable. A mathematical definition given by DeGroot in "Probability and Statistics" A real valued function that is defined in space S is called a random variable. For each random variable X and each set A of real numbers, we could calculate the probabilities. The collection of all of these probabilities is the distribution of X. Triola gets accross the idea of a collection as a table, graph or formula. Further to the definition is the types of distributions- discrete or continuous. Some well know distribution are the normal distribution, exponential, binomial, uniform, triangular and Poisson.
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
