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What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
How do you calculate probability given mean and standard deviation?
The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question.
Is the mean of probability distribution is called its expected value?
No. The mean is the expected value of the random variable but you can also have expected values of functions of the random variable. If you define X as the random variable representing the result of a single throw of a fair die, the expected value of X is 3.5, the mean of the probability distribution of X. However, you play a game where you pay someone a certain amount of money for each throw of the die and the other person pays you your "winnings" which depend on the outcome of the throw. The variable, "your winnings", will also have an expected value. As will your opponent's winnings.
What does it mean normal distribution?
The Normal distribution is a probability distribution of the exponential family. It is a symmetric distribution which is defined by just two parameters: its mean and variance (or standard deviation. It is one of the most commonly occurring distributions for continuous variables. Also, under suitable conditions, other distributions can be approximated by the Normal. Unfortunately, these approximations are often used even if the required conditions are not met!
From a uniform distribution why is the total area under the curve equal to 1?
Because the area under the curve is a probability and probabilities range from 0.00 to 1.00 or could also be written as 0% to 100%
What is of discrete uniform distribution?
A discrete uniform distribution assigns the same probability to two or more possible events. For example, there is a discrete uniform distribution associated with flipping a coin: 'heads' is assigned a probability of 1/2 as is the event 'tails'. (Note that the probabilities are equal or 'uniform'.) There is also a discrete uniform distribution associated with tossing a die in that there is a 1/6 probability for seeing each possible side of the die.
Is normal distribution also a probability distribution?
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
Why is the normal probability distribution called a family of normal probability distribution?
Because very many variables tend to have the Gaussian distribution. Furthermore, even if the underlying distribution is non-Gaussian, the distribution of the means of repeated samples will be Gaussian. As a result, the Gaussian distributions are also referred to as Normal.
What type of probability distribution is the normal distribution?
It is a continuous parametric distribution belonging to the family of exponential distributions. It is also symmetric.
Can the mean of a discrete variable like the number of children be normally distributed?
Not really. The distribution is not only discrete but also heavily skewed. However, the average number of children in sets of families can be approximated by the normal distribution.
If a probability distribution curve is bell-shaped then this is a normal distribution?
True * * * * * No. The Student's t-distribution, for example, is also bell shaped.
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
The normal distribution, also known as the Gaussian distribution, has a familiar "bell curve" shape and approximates many different naturally occurring distributions over real numbers.
Why is the probability of an event always a number between 0 and 1?
The probability of an event is defined as the ratio of favourable outcomes to total outcomes. In the case of discrete distributions these will be represented by numbers, while for continuous distribution they will be measured as areas. In either case, the first measure is non-negative and the second is positive and so the probability is greater than 0. Also, the number of favourable outcomes cannot be greater than the total so the probability must be at most 1.
Example of median of continuous data?
a discrete probability distribution, a median m satisfies the inequalitiesorin which a Lebesgue-Stieltjes integral is used. For an absolutely continuous probability distribution with probability density function ƒ, we have[edit]Medians of particular distributionsThe medians of certain types of distributions can be easily calculated from their parameters:The median of a normal distribution with mean μ and variance σ2 is μ. In fact, for a normal distribution, mean = median = mode.The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean.The median of a Cauchy distribution with location parameter x0 and scale parameter y is x0, the location parameter.The median of an exponential distribution with rate parameter λ is the natural logarithm of 2 divided by the rate parameter: λ−1ln 2.The median of a Weibull distribution with shape parameter k and scale parameter λ is λ(ln 2)1/k.
Discrete packages of light energy are called what?
Discrete packages of light energy are called photons. Photons are the smallest discrete unit of light and exhibit both wave-like and particle-like properties.
What does mu mean in statistics?
Usually mu is the symbol for the mean of a probability distribution. It is sometimes used as the average of a dataset (also called the mean of the dataset), although I prefer to use "x bar".
What is the probability density of the wave function?
See related link, In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density. For example, the values taken by a normalised wave function ψ are amplitudes, since |ψ(x)|2 gives the probability density at position x. Probability amplitudes may also correspond to probabilities of discrete outcomes.
