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in exercises consider an urn containing 12 balls numbered 1 to 12 further the balls numbered 1 to 8 are white and the
given jointly distributed random variables x1nbspand x2 prove that for any x2nbspand almost all x1nbsp fx2x2x2 x1
in exercises let x and y be independent random variables let z y - x let a y - x le 1 find i pax 1 ii fzix01
in exercises let x and y be independent random variables let u x y and v y - x let a v le 1 find i pau 1 ii fvu01
consider the events a and b defined in example la assuming that pa pb frac12 pab 13 find the probability for k 0 12
the amount of bread in hundreds of pounds that a certain bakery is able to sell in a day is found to be a
let x1 x2 xnnbspbe independent random variables uniformly distributed over the interval 0 to 1 describe the
let x and y be independent random variables each exponentially distributed with parameter a find the probability
show that if x1 x2nbsp xnnbspare independent identically distributed random variables whose minimum y minimum x1
determine how large a random sample one must take of a random variable uniformly distributed on the interval 0 to i in
the random variable x represents the amplitude of a sine wave y represents the amplitude of a cosine wave both are
let x1nbspand x2nbspbe independent random variables each exponentially distributed with parameter lambda frac12 find
let t be a random variable and let t be a fixed number define the random variable u by u t - t and the event a by a t
if x and yare independent poisson random variables show that the conditional distribution of x given x y is
show that if x1nbsphas a poisson distribution with parameter a1 if x2nbsphas a poisson distribution with parameter
prove the validity of the assertion made in example 91 identify the probability law of y find the probability law of z
prove that it is impossible for two independent identically distributed random variables x1nbspand x2 each taking the
suppose that the load on an airplane wing is a random variable x obeying a normal probability law with mean 1000 and
in exercises let x1nbspand x2nbspbe independently and uniformly distributed over the intervals 0 to 1find and sketch
in exercises let x1nbspand x2nbspbe independently and uniformly distributed over the intervals 0 to 1i maximum x1 x2 ii
in exercises let x1nbspand x2nbspbe independently and uniformly distributed over the intervals 0 to 1i x1 x2 ii
let x1 x2 and x3 be independent random variables each exponentially distributed with parameter a frac12 find the
find and sketch the probability density function of theta tan-1 yx if x and yare independent random variables each
the envelope of a narrow-band noise is sampled periodically the samples being sufficiently far apart to assure
let v vx2nbsp vy2nbsp vz2frac12nbspbe the magnitude of the velocity of a particle whose velocity components vx vy