Question

(5) 2. 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: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities.

Answer 1

a) below is distribution table forx1,x2x3 P(x1x2,x3) xbar 0.027 0.018 0.045 0.018 0.012 0.030 0.045 0.030 0.075 0.018 0.012 0.030 0.012 0.008 0.020 0.030 0.020 0.050 0.045 0.030 0.075 0.030 0.020 0.050 0.075 0.050 0.125 1000 1.333 1667 1.333 1667 2.000 1667 2.000 2.333 1.333 1667 2.000 1667 2.000 2.333 2.000 2.333 2.667 1667 2.000 2.333 2.000 2.333 2.667 2.333 2.667 3.000 2 2 2 2 2 2

from above: pmf of xn is as follows: P(xbar) 0.027 0.054 1000 1.333 1667 2.000 2.333 2667 3.000 0.188 0.285 0.150

P(xbar) 0.300 0.250 0.200 0.150 0.100 0.050 0.000 .000 1333 1.667 2000 2.333 2.6673.000 Pixbar) Ь) smallest value of S2 is O for which probability is Plall three values are same)-(0.33-0.2 0.53-016 2nd smallest value of s2 is 0.333 for which probability is-0.09