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the number of marriage licenses issued in a certain city during the month of june may be looked upon as a random
a study of the nutritional value of a certain kind of bread shows that the amount of thiamine vitamin b1 in a slice may
with reference to exercise 71 what can we assert about the amount of time it takes a person to be served at the given
a quarter is bent so that the probabilities of heads and tails are 040 and 060 if it is tossed twice what is the
the inside diameter of a cylindrical tube is a random variable with a mean of 3 inches and a standard deviation of 002
the length of certain bricks is a random variable with a mean of 8 inches and a standard deviation of 01 inch and the
if heads is a success when we flip a coin getting a six is a success when we roll a die and getting an ace is a success
the amount of time in minutes that an executive of a certain firm talks on the telephone is a random variable having
probabilitymaximum and minimum temperaturessearch the internet for us climate datachoose the city in which you
we did not study the bernoulli distribution in any detail in section 3 because it can be looked upon as a binomial
an alternative proof of theorem 2 may be based on the fact that if x1 x2 and xn are independent random variables
when calculating all the values of a binomial distribution the work can usually be simplified by first calculating b0 n
use the recursion formula of exercise 8 to show that for theta 12 the binomial distribution hasexercise 8when
in the proof of theorem 2 we determined the quantity exx - 1 called the second factorial moment in general the rth
the factorial moment-generating function of a discrete random variable x is given byshow that the rth derivative of fxt
with reference to exercise 12 find the factorial moment-generating function ofa the bernoulli distribution and show
the negative binomial distribution is sometimes defined in a different way as the distribution of the number of
with reference to exercise 16 find expressions for muy andnbspexercise 16the negative binomial distribution is
if the probability is fx that a product fails the xth time it is being used that is on the xth trial then its failure
a variation of the binomial distribution arises when the n trials are all independent but the probability of a success
when calculating all the values of a poisson distribution the work can often be simplified by first calculating p0
suppose that fx t is the probability of getting x successes during a time interval of length t when i the probability
use repeated integration by parts to show thatthis result is important because values of the distribution function of a
show that if the limiting conditions n rarrinfin theta rarr0 while ntheta remains constant are applied to the
differentiating with respect to lambda the expressions on both sides of the equationderive the following recursion