I have a test coming up and wanted to know of the following, when to use each on

Question

I have a test coming up and wanted to know of the following, when to use each one:
1) Regular Continous RV
2) Normal Distribution
3) Exponential Distribution
4) and Lognormal Distribution

THanks

Explanation / Answer

A continuous random variable maps outcomes to values of an uncountable set .... that is answered by the variance and standard deviation of a random variable. variance of a continuous RV and some useful properties,. 3. mean and variance of uniform, exponential and Gaussian (normal) RVs,. 4. a (linear ... The use of the term “expected value” does not mean that we expect to observe E[X] 2 In probability theory, the normal (or Gaussian) distribution is a continuous probability distribution that has a bell-shaped probability density function Normal distributions have many convenient properties, so random variates with unknown distributions are often assumed to be normal, especially in physics This guide will show you how to calculate the probability (area under the curve) of a standard normal distribution. It will first show you how to interpret a Standard Normal Distribution Table. It will then show you how to calculate the: probability less than a z-value probability greater than a z-value probability between z-values probability outside two z-values. 3 In probability theory and statistics, the exponential distribution (a.k.a. negative exponential distribution) is a family of continuous probability distributions. It describes the time between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate. It is the continuous analogue of the geometric distribution. Note that the exponential distribution is not the same as the class of exponential families of distributions, which is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes the normal distribution, binomial distribution, gamma distribution, Poisson, and many others. 4 The Lognormal distribution is useful for modeling naturally occurring variables that are the product of a number of other naturally occurring variables. Jump to: navigation, search Log-normal Probability density function Some log-normal density functions with identical location parameter µ but differing scale parameters s Cumulative distribution function Cumulative distribution function of the log-normal distribution (with µ = 0 ) Notation lnmathcal{N}(mu,,sigma^2) Parameters s2 > 0 — shape (real), µ ? R — log-scale Support x ? (0, +8) PDF rac{1}{xsqrt{2pisigma^2}}, e^{-rac{left(ln x-mu ight)^2}{2sigma^2}} CDF rac12 + rac12,mathrm{erf}Big[rac{ln x-mu}{sqrt{2sigma^2}}Big] Mean e^{mu+sigma^2/2} Median e^{mu}, Mode e^{mu-sigma^2} Variance (e^{sigma^2}!!-1) e^{2mu+sigma^2} Skewness (e^{sigma^2}!!+2) sqrt{e^{sigma^2}!!-1} Ex. kurtosis e^{4sigma^2}!! + 2e^{3sigma^2}!! + 3e^{2sigma^2}!! - 6 Entropy rac12 + rac12 ln(2pisigma^2) + mu MGF (defined only on the negative half-axis, see text) CF representation sum_{n=0}^{infty}rac{(it)^n}{n!}e^{nmu+n^2sigma^2/2} is asymptotically divergent but sufficient for numerical purposes Fisher information egin{pmatrix}1/sigma^2&0\0&1/(2sigma^4)end{pmatrix} In probability theory, a log-normal distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. If X is a random variable with a normal distribution, then Y = exp(X) has a log-normal distribution; likewise, if Y is log-normally distributed, then X = log(Y) has a normal distribution. The log-normal distribution is the distribution of a random variable that takes only positive real values.

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