Question

Let x be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of x is as follows: x 1 2 3 p (x) 0.3 0.5 0.2 if a random sample of size n = 2 is selected,
a.What is p ( x = 2 ) ?
b.Find the pmf of the sample variance ( n = 2 ) .
c.If a random sample of size n = 3 is selected, what is p ( x 1.6 ) ?

Answer 1

Answer:

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. 1 2 X 3 4 p(x) 0.2 0.1 0.3 0.4 (a) Consider a random sample of sizen 2 (two customers), and let X be the sample mean number of packages shipped. Obta the probability distribution of X. 4 3.5 3 1.5 2 2.5 PCR) (b) Refer to part (a) and calcu late P(X s 2.5). (c) 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 1 2 P(R) (d) If a random sample of size n 4 is selected, what is P(X s 1.5)? [Hint: You should not have to list all possible outcomes, only those for which x s 1.5.]