Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. x 1 2 3 4 p(x) 0.1 0.2 0.3 0.4   (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.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows.
x 1 2 3 4
p(x)
0.1 0.2 0.3 0.4

 

(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.
x 1 1.5 2 2.5 3 3.5 4  
P(x)              

 

b) Again consider a random sample of size n = 2, but now focus on the statistic R = the sample range (difference between the largest and smallest values in the sample). Obtain the distribution of R. [Hint: Calculate the value of R for each outcome and use the probabilities from part (a).]
R 0 1 2 3
P(R)        
(d) If a random sample of size n = 4 is selected, what is P(X ≤ 1.5)?
 [Hint: You should not have to list all possible outcomes, only those for which x ≤ 1.5.]
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