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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
if the probability is 075 that a person will believe a rumor about the transgressions of a certain politician find the