Let X be the numbe of packages being mailed by a randomly selected customer at a

Question

Let X be the numbe of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of Xis as Tollows )|0.2 0.3 0.4 0.1 (a) Consider a random sample of size n - 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X. 1.5 2.5 2.5 D(x) ,04 12 25 .28 08 (b) Refer to part (a) and calculate p( 7.5). (c) Again concider a rondom sample af siza n- 2, but now focus on the statistic R the sampla range (differance batween the largest and smallest valucs in the sample). Obtain the distribution of R. Hint: Calculate the valus of R for cach outcome and use the probabilities trom part (a).J (d) ifa random sample of size n-4 is selected, what is s 15)? [Hint: You should not have to list all possible outcomes, anly those for which x s 1.5] 25

Explanation / Answer

c) for given probability distribution :

P(Xbar<=1.5) =P(all 4 are 1; 3 are 1 and one 3 ; 2 1's and 2 2's ; 3 1's and 1 2)

=0.24 +4*(0.2)3*0.4+6*(0.2)2*(0.3)2+4*(0.2)2*(0.3)  =0.0456

x1 x2 Range( R) P( R) 1 1 0 0.04 2 1 1 0.06 3 1 2 0.08 4 1 3 0.02 1 2 1 0.06 2 2 0 0.09 3 2 1 0.12 4 2 2 0.03 1 3 2 0.08 2 3 1 0.12 3 3 0 0.16 4 3 1 0.04 1 4 3 0.02 2 4 2 0.03 3 4 1 0.04 4 4 0 0.01

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