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
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.
How to find the distribution of a function of a random variable with known distribution. The general case, the discrete case, the continuous case.
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...
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...
The following functions give a random variate from a specified distribution. The arguments are the parameters of the distribution. You can repeat the sequence of pseudorandom numbers by setting a seed in the Preferences dialog box before each sequence. Note the period in each function name. ...
The moment generating function or MGF is used to find moments for random variables. Due to its uniqueness property, it is used to find the probability distribution of a function of random variables. The probability generating function is used to find probabilities ...
To compare results of the function for Excel 2003 and later versions of Excel with results of the function when it is used in earlier versions of Excel More Information NORMSINV(p) returns the value z such that, with probability p, a standard normal random variable takes on a value that ...
To compare results of the function for Excel 2003 and later versions of Excel with results of the function when it is used in earlier versions of Excel More Information NORMSINV(p) returns the value z such that, with probability p, a standard normal random variable takes on a value that is...