(10) Suppose that, on average, 3 telemarketers call your house during a 7-day pe
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(10) Suppose that, on average, 3 telemarketers call your house during a 7-day period. What is the probability that no telemarketer call your house on a given day? Assume that the number of telemarketers per day follow:s Poisson distribution (11) Suppose that, during a given week, 5,000, 000 people play a lottery game. If their chances to win the lottery are independent, and if each person has probably 1/2,000, 000 of winning the lottery, write an exact expression for the probability that there are exactly 4 winners of the lottery that week Moreover, give an approximate value for the probability that there are exactly 4 winners (12) Suppose that X is a Poisson random variable with E(X] = . Find E X(X - 1) (X - 2)Explanation / Answer
10)average number of calls in a given day =3/7 =
probability that no telemarketers call your house =P(X=0)=e-x/x!=0.6514
11)
probability that there are exactly 4 winners =P(X=4)=5000000C4 (1/2000000)4(1-1/2000000)5000000-4
here expected number of people to win lotteery =np=(5000000)(1/2000000)=2.5=
therefore from poisson approximation probability that 4 people won =P(X=4) =e-x/x!= 0.1336
12 ) here for poisson distribution E(X)=
and E(X2)=2+
E(X3) =+32+3
E(X(X-1)*(X-2)) =E((X2-X)*(X-2)) =E(X3-2X2-X2+2X)=E(X3-3X2+2X)=E(X3)-3E(X2)+2E(X) =
=+32+3 -3(2+)+2 =3
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