Question

Table 1: First 6 entries of the probability model circumscribing the number of units of book-cases that will be demanded per month. Caution for the full model please consult the RegIndust.csv file.

X	PrX
100	0.331595
300	0.255816
650	0.091957
800	0.161964
850	0.141161
1050	0.014922
1400	0.002586

(a) (1 point) Is the full probability model proper ? Justify your answer.

(b) (1 point) Please determine the expected value for X.

(c) (2 points) Determine the standard deviation for X. (

d) (1 point) Determine the coefficient of variation for X

Answer 1

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All calculation are done in the table. Follow the detailed explanation below and the table to get answer.

a) we will addup all p(x)s and check if they all add to a 1. if they do, then its a valid full and proper probability model. We do see a sum of 1 when we add up.

Answer: So, YES, it is a full and proper probability model ( Check in 3rd column)

b) Expected value is probability p(x) weighted value of x. It is computed as E(x) in the 4th column.

Answer: Expected value of X = 438.5229

c) The standard deviation is given by : sqrt(E(x^2) - E(x)^2). We calculate x^2, and take its probability weigted value to get E(x^2) in column 5th. Then we subtract E(x)^2 and take a square root of the this subtraction result to get Standard deviation value of x.  This is in column 6th.

Answer: Standard deviation for x is : 316.3143

d) Coefficient of variation is (Standard deviation/Expected Value) * 100%. This is calculated in 7th column.

Answer: coefficient of variation for x is : 72.13%

Table with all calculations: