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Does finite variance imply finite mean?
Assume that a random variable has a finite variance. Does it mean it also has a finite mean? My approach: I think since it has a finite variance, it means it is in L2 space of the probability measure μ. Therefore, it should be in L1 space of the probability measure μ and thus the mean is finite.
Can a distribution be symmetric but not normal?
A normal distribution is the proper term for a probability bell curve. In a normal distribution the mean is zero and the standard deviation is 1. Normal distributions are symmetrical, but not all symmetrical distributions are normal. In reality, most pricing distributions are not perfectly normal.
What is an example of a probability distribution that has a finite mean but infinite variance?
A distribution with finite mean and infinite variance. Examples: t2 distribution. Pareto with α=32.
Can variance not exist?
The lack of a mean and variance for a Cauchy distribution. Not every distribution has a mean and variance. There are also distributions that have means but not variances, or, you could say, their variances are infinite.
What does it mean to have finite variance?
1. Important point: if variance of a population is infinite, but variance of a sample is finite, then any estimate of the population’s variance or standard deviation using a sample statistic like s2, or s, then s√n will be rather badly biased.
What distribution has highest variance?
normal distribution
The normal distribution has the maximum entropy among all continuous distributions with fixed mean and variance on real support. The variance for a given entropy can be made arbitrarily large using a mixture of two Gaussians that are spread farther and farther apart.
How do you know if a distribution is symmetric?
A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other. The mean, the median, and the mode are each seven for these data.
Can a distribution have infinite variance?
Models with infinite variance have right tails that extend to infinity. Variance is a measure of how spread out a distribution is. Distributions with infinite variance have fat upper tails that decrease at an extremely slow rate.
Which distribution has the largest variance?
Although the data follows a normal distribution, each sample has different spreads. Sample A has the largest variability while Sample C has the smallest variability.
How do you find the continuous variance?
Definition: Let X be a continuous random variable with mean µ. The variance of X is Var(X) = E((X − µ)2). These are exactly the same as in the discrete case.