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)...
5. Functions of a Random VariableLebanon, Guy
How to find the distribution of a function of a random variable with known distribution. The general case, the discrete case, the continuous case.
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.
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...
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 ...
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...
Lower and upper bounds for the variance (that is the mean deviation in $\L_2$) of functions of a random variable are well-known in the literature where they are called Cacoullos, Chernoff, or Poincar\'e type inequality. A similar upper bound is known for the mean deviation of functions...
If we sett= 0 in the above formulas, then theetxterm becomese0= 1. Thus we obtain formulas for the moments of the random variableX: M’(0) =E(X) M’’(0) =E(X2) M’’’(0) =E(X3) M(n)(0) =E(Xn) This means that if the moment generating function exists for a particul...
Power system reliabilityProbability distributionRandom variablesIn finding the distribution of a function of a scalar or vector random variable the following formulas turn out to be very useful.doi:10.1007/978-1-4612-4526-1_7T. CacoullosSpringer New York...