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show that jf the additivity property holds then the homogeneity property holds for all rational numbers alpha thus if a
consider a sample x1 xn of normally distributed random variables with mean mu and variance sd2 1a if n 10 what is
let x1 x2 x3nbspbe jointly distributed random variables with zero means unit variances and covariances cov x1 x2 080
the probability that a vending machine in the oxnard university student center will dispense the desired item when
you are shown a coin that its owner says is fair in the sense that it will produce the same number of heads and tails
a man with n keys wants to open his door he tries the keys independently and at random let nnnbspbe the number of
the game of roulette is described in example id find the probability that the total amount of money lost by a gambling
a man plays a game in which his probability of winning or losing a dollar is t let s be the mans fortune that is the
consider a game of chance in which one may win 10 dollars or lose 1 2 3 or 4 dollars each possibility has probability
a certain gamblers daily income in dollars is a random variable x uniformly distributed over the interval -3 to 3i find
add 100 real numbers each of which is rounded off to the nearest integer assume that each rounding-off error is a
if each strand in a rope has a breaking strength with mean 20 pounds and standard deviation 2 pounds and the breaking
consider light bulbs produced by a machine whose life x in hours is a random variable obeying an exponential
a man invests a total of n dollars in a group of n securities whose rates of return interest rates are independent
a random variable xhas an unknown mean and known variance 4 how large a random sample should one take if the
consider a gas composed of molecules with mass of the order of 10-24 grams and at room temperature whose velocities
in an urn containing n balls a proportion p is white and q 1 - p are black a ball is drawn and its color noted the
consider 2 events a and b such that pa frac14 pba to pab frac12 define random variables x and y x i or 0 depending
consider a sample of size 2 drawn with replacement without replacement from an urn containing 4 balls numbered 1 to 4
two fair coins each with faces numbered 1 and 2 are thrown independently let x denote the sum of the 2 numbers obtained
let u v and w be uncorrelated random variables with equal variances let x u v y u w find the correlation
let x1 and x2 be uncorrelated random variables find the correlation py1 y2 between the random variables y1 x1 x2 and
let x1nbspand x2nbspbe uncorrelated normally distributed random variables find the correlation py1nbsp y2 between the
the mean and variance of the number of matches let sill be the number of matches obtained by distributing 1 to an urn m
consider a sequence of independent repeated bernoulli trials in which the probability of success on any trial is p