Search results
Results from the WOW.Com Content Network
Probability theory. In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode ), while ...
The median of a normal distribution with mean μ and variance σ 2 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 x 0 and scale parameter y is x 0, the location parameter.
The mean of a probability distributionis the long-run arithmetic average value of a random variablehaving that distribution. If the random variable is denoted by X{\displaystyle X}, then the mean is also known as the expected valueof X{\displaystyle X}(denoted E(X){\displaystyle E(X)}).
The mass of probability distribution is balanced at the expected value, here a Beta(α,β) distribution with expected value α/(α+β). In classical mechanics, the center of mass is an analogous concept to expectation. For example, suppose X is a discrete random variable with values x i and corresponding probabilities p i.
The Poisson distribution is an appropriate model if the following assumptions are true: k is the number of times an event occurs in an interval and k can take values 0, 1, 2, ... . The occurrence of one event does not affect the probability that a second event will occur. That is, events occur independently.
This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean.
Log-normal distribution. In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution.
The binomial distribution is the PMF of k successes given n independent events each with a probability p of success. Mathematically, when α = k + 1 and β = n − k + 1, the beta distribution and the binomial distribution are related by [clarification needed] a factor of n + 1 :