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nbspa certain class of students takes a standardized test where each students score is modeled as a random variable
letnbsp xknbspbe a sequence of iid exponential random variables with mean of 1 we wish tonbspa find a bound to the
suppose we wish to estimate the probabilitypa of some event a we do so by repeating an experiment times and observing
the traffic managers of toll roads and toll bridges need specific information to properly staff the toll booths so that
a sequence of zero mean unit variance independent random variablesnbspnbspare input to a filter that produces an output
let xy andnbsp z be a set of independent zero-mean unit-variance gaussian random variables form a new set of random
a random variable x has a gaussian pdf with mean 5 and unit variance we measure 10 independent samples of the random
two independent samples of a random variablenbsp x are takendetermine the expected value and variance of the sample
the noise level in a room is measured nnbsp timesthe error or each measurement is independent of the others and is
suppose x is a vector of iid random variables where each element has some pdfnbspnbspfind an example pdf such that the
suppose the variance of an iid sequence of random variables is formed according towhere micronbsp is the sample mean
simple linear regression -problem definition midwest insurance wants to develop a model able to predict sales according
find the variance of the sample standard deviationassuming that the xinbspnbspnbspiid gaussian random variables with
a sequence of random variables xnnbspis to be approximated by a straight line using the estimatenbspnbspdetermine the
a vector random variable x has a mean vector and correlation matrix given bya new random vector is formed according
let x be a two-element zero-mean random vector suppose we construct a new random vector y according to a linear
a three-dimensional vector random variable x has a covariance matrix offind a transformation matrix a such that the new
supposenbspnbspare a sequence of independent and exponentially distributed random variables withassuming that is an odd
letnbspnbspbe a sequence of five independent discrete random variables each with a distribution described bya find the
a set of nnbsp random variablesnbspx1 x2 x3xn are independent and each uniformly distributed overnbspa find the
a random vector is generated by rolling a die and observing the outcome the components of the random vector are
consider a vector of n random variablesnbspnbspsuppose we form a new random variablenbsp z by performing a weighted
letnbspnbsprepresent an n-dimensional vector of random variables that is uniformly distributed over the regionnbspthat
letnbspnbsprepresent a three-dimensional vector of random variables that is uniformly distributed over the unit sphere
suppose a point in three-dimensional cartesian space x y znbsp is equally likely to fall anywhere on the surface of the