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Should you use the Binomial Normal or Poisson distribution if in the past few years an average of 10 businesses closed and I want to find the probability of more than 10 businesses closing next year?
If this is the only information that you have then you must use the Poisson distribution.
What is a random variable in probability theory?
Random Variable in probability theory is defined as follows: Assuming you have variables Xi where i is an integer ie: i=1,2,3.......n a variable Xi is called a random variable iff(if and only iff) and random selection yields a variable Xi for i=1,2.........,n with the same likelihood of appearance. i.e prob(X=Xi)=1/n
What are two requirements for a discrete probability distribution?
Not sure about only two requirements. I would say all of the following:there is a finite (or countably infinite) number of mutually exclusive outcomes possible,the probability of each outcome is a number between 0 and 1,the sum of the probabilities over all possible outcomes is 1.The Poisson distribution, for example, is countably infinite.
What is the probability of not geeting a queen in a well shuffled deck of 52 playing cards?
If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.If only one card is selected the probability is 12/13.
If an event has a 1 in 4 chance of occurring what is the probability of it happening to one individual in a sample of five?
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
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.
Should you use the Binomial Normal or Poisson distribution if in the past few years an average of 10 businesses closed and I want to find the probability of more than 10 businesses closing next year?
If this is the only information that you have then you must use the Poisson distribution.
What is a random variable in probability theory?
Random Variable in probability theory is defined as follows: Assuming you have variables Xi where i is an integer ie: i=1,2,3.......n a variable Xi is called a random variable iff(if and only iff) and random selection yields a variable Xi for i=1,2.........,n with the same likelihood of appearance. i.e prob(X=Xi)=1/n
What percent probability is associated with a z-value of 1.3?
None. The probability of a continuous variable taking any particular value is always zero. The probability is greater than zero only when an interval (or range) is specified.
What does it mean to solve a formula for a variable that appears on both sides?
It means that you manipulate the equation in such a way that the variable appears only on one side, by itself.
Why binomial distribution can be approximated by Poisson distribution?
Only in certain circumstances:The probability of success, p, in each trial must be close to 0.Then, for the random variable, X = number of successes in n trials, the mean is npand the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.Only in certain circumstances:The probability of success, p, in each trial must be close to 0.Then, for the random variable, X = number of successes in n trials, the mean is npand the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.Only in certain circumstances:The probability of success, p, in each trial must be close to 0.Then, for the random variable, X = number of successes in n trials, the mean is npand the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.Only in certain circumstances:The probability of success, p, in each trial must be close to 0.Then, for the random variable, X = number of successes in n trials, the mean is npand the variance is np(1-p). But since p is close to 0, (1-p) is close to 1 and so np(1-p) is close to np.That is, the mean of the distribution is close to its variance. This is a characteristic of the Poisson distribution.Furthermore, the other characteristics of the distribution: constant probability, independence are met so the Binomial can be approximated by the Poisson.It is possible to prove this analytically but the limitations of this browser - especially in terms of mathematical notation - preclude that.
The probability that a standard normal random variable Z is less than 50 is approximately 0?
False. It is approximately 1. Theoretically, it is not 1. I used excel, and I know the probability is between 0.999999 and 1. as the probability of Z<6 is 0.999999. I can't calculate the probability exactly because excel only goes to 7 place accuracy.
What are two requirements for a discrete probability distribution?
Not sure about only two requirements. I would say all of the following:there is a finite (or countably infinite) number of mutually exclusive outcomes possible,the probability of each outcome is a number between 0 and 1,the sum of the probabilities over all possible outcomes is 1.The Poisson distribution, for example, is countably infinite.
What is the difference between a discrete and a continuous probability function?
A discrete random variable (RV) can only take a selected number of values whereas a continuous rv can take infinitely many.
Which kind of formula provides the most information?
The mutual information formula provides the most information, quantifying the amount of information that one random variable contains about another. It measures the reduction in uncertainty of one variable given the knowledge of another variable.
Are the mean and standard deviation equal in a poisson distribution?
The mean and variance are equal in the Poisson distribution. The mean and std deviation would be equal only for the case of mean = 1. See related link.
What is a frequency distribution defined by its average and standard deviation?
The triangular, uniform, binomial, Poisson, geometric, exponential and Gaussian distributions are some that can be so defined. In fact, the Poisson and exponential need only the mean.
