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a students final exam grade depends on how close the student sits to the center of the classroom during lectures if a
a business trip is equally likely to take 2 3 or 4 days after a d-day trip the change in the travelers weight measured
let h and b be the random variables in quiz 43 find rhb and covh bquiz 43the probability mass function phbh b for the
for the random variables x and y in problem 421 finda the expected value of w yxb the correlation exyc the covariance
in a simple model of a cellular telephone system a portable telephone is equally likely to be found anywhere in a
for random variables x and y given in problem 464 what is the pmf of v maxx yproblem 464let x and y be discrete random
let x and y be discrete random variables with joint pmf pxynbspx y that is zero except when x and y are integers let w
given random variables x and y in problem 421 and the function w x - y finda the probability mass function pwnbspwb
given the random variables x and y in problem 421 finda the marginal pmfs pxnbspx and pynbspyb the expected values ex
each test of an integrated circuit produces an acceptable circuit with probability p independent of the outcome of the
as a generalization of example 41 consider a test of n circuits such that each circuit is acceptable with probability p
in figure 42 the axes of the figures are labeled x and y because the figures depict possible values of the random
test two integrated circuits in each test the probability of rejecting the circuit is p let x be the number of rejects
in this problem we prove theorem 45a sketch the following events on the x y planeb express the probability of the
write a matlab program that simulates m runs of the weekly lottery of problem 555 for m 1000 sample runs form a
we continue problem 582 where the vector x of finish times has correlated components let w denote the finish time of
for the vector of daily temperatures t1nbspmiddotmiddotmiddot t31 and average temperature y modeled in quiz 58 we wish
a better model for the sailboat race of problem 554 accounts for the fact that all boats are subject to the same
consider the vector x in problem 571 and define the average to be y x1nbsp x2nbsp x33 what is the probability that y
in this problem we extend the proof of theorem 516 to the case when a is m times n with mnbspxnbsp 0a prove there
an n-dimensional gaussian vector w has a block diagonal covariance matrix where cx is m times m cynbspis n - m times n
x x1nbspx2 is a gaussian 0 cx vector wherethus depending on the value of the correlation coefficient rho the joint pdf
let x be a gaussian microx cx random vector let y ax where a is an m timesn matrix of rank m by theorem 516 y is a
given the gaussian random vector x in problem 571 y ax b whereand b -4 -4 -4 calculatea the expected value microyb
as in quiz 51 and example 55 the 4-dimensional random vector y has pdffind the expected value vector ey the correlation