Question

The demand, D, for parts at a repair bench per day can be described by the following discrete PMF:

D	0	1	2
p(D)	0.3	0.2	0.5

Generate the demand for the first 4 days using the following numbers (starting with the first row)

.943	.398	.372	.943	.204	.794
.498	.528	.272	.899	.294	.156
.102	.057	.409	.398	.400	.997

Answer 1

The given PMF ( probability mass function) of a repair bench per day is as follows:

PMF:

D	0	1	2
p(D)	0.3	0.2	0.5

Let's find distribution function of D

PMF:

D	0	1	2
F(D)	0.3	0.5	1.0

We want to generate the demand for the first 4 days :

The first number in the first row is 0.943

From the cumulative distribution function, we have P( D <= 1) = 0.5 < 0.943 < P( D < = 2) = 1

Therefore for first day the demand D = 2

Then 2nd number in the firsrt row is 0.398. Since,

P( D <= 0) = 0.3 < 0.398 < P( D < = 1) = 0.5

We select demand for 2nd day as D = 1

The 3rd number in the first column is 0.372.

Since,

P( D <= 0) = 0.3 < 0.372 < P( D < = 1) = 0.5

We select demand for 3rd day as D = 1

The fourth number in the first column is 0.943.

Since P( D <= 1) = 0.5 < 0.943 < P( D < = 2) = 1

We select demand for 4th day as D = 2

So demand selected in first, second, third, and fourth days are 2, 1, 1, and 2 respectively.