In many practical problems, especially in mathematical statistics, it is necessary to know how to find the distribution of a function of a random variable. The probability of occurrence of the random variables Y = 蠁(x) in a set B is equal to the probability of occurrence of the random ...
When is a discrete random variable, the probability mass function of can be computed as follows. Proposition (probability mass of a decreasing function) Let be a discrete random variable with support and probability mass function . Let be strictly decreasing on the support of . Then, the ...
Theorem Function of a Discrete Random Variable. LetXXhave a discrete distribution with p.f.ffand letY=r(X)Y=r(X)for some function ofrrdefined on the set of possible values ofXXFor each possible value y ofYYthe p.f.ggofYYis g(y)=Pr(Y=y)=Pr[r(X)=y]=∑x;r(x)=yf(x)g(y)...
Consider the notion of a "square-law" detector: If x is an input to the detector, then y = x2 is its output or detected value. Consider next the case where x is a random variable with probability law ...Frieden, B. RoyThe University of Arizona...
A random variable is a rule that assigns a numeric value to every possible outcome in a sample space. Random variables may be discrete or continuous in nature. A random variable is discrete if it assumes only discrete values within a specified interval.
Sometimes experiments do not directly measure the quantity of interest, but rather associated variables that can be related to the one of interest by an analytic function. It is therefore necessary to establish how we can infer properties of the interesting variable based on properties of the ...
This means that if the moment generating function exists for a particular random variable, then we can find its mean and its variance in terms of derivatives of the moment generating function. The mean isM’(0), and the variance isM’’(0) – [M’(0)]2. ...
Law of the unconscious statistician (LOTUS) for two discrete random variables: E[g(X,Y)]=∑(xi,yj)∈RXYg(xi,yj)PXY(xi,yj)(5.5)E[g(X,Y)]=∑(xi,yj)∈RXYg(xi,yj)PXY(xi,yj)(5.5) Example Linearity of Expectation: XX
Numeric. Returns a random value from a chi-square distribution with specified degrees of freedom df. RV.EXP. RV.EXP(scale). Numeric. Returns a random value from an exponential distribution with specified scale parameter. RV.F. RV.F(df1, df2). Numeric. Returns a random value from an F ...
CHAPTER 4 – CHARACTERISTIC FUNCTIONS OF A RANDOM VARIABLE The results of an experimental investigation on the effect of a vortex generator in the form of a mechanical tab placed at the nozzle exit on the evolution... V. Pugachev - Elsevier Ltd 被引量: 0发表: 1965年 Numerical inversion of...