Question

A home bakery company sells donuts in a box that has a varied taste. From the data it turns out that the sales form a uniform discrete distribution with a maximum sales of 100 units and a minimum of 40 units per day. Forms of discrete uniform functions as follows: F(X)-|b for a SX b + 1 +1 others The question is If used random number with data a 77, m -127, Zo 12357, calculate 5 times to know the sale?

Answer 1

the random number generator given is

where a=77, m=127 and the first value for n=0 is

We will generate 5 random numbers as below

• 
• 
• 
• 
• 

To convert these numbers in the interval (0,1) we divide these by m=127

• 
• 
• 
  из 54/127= 0.4252
  
• $u_{4}=94/127=0.7402$
• $u_{5}=126/127=0.9921$

Next to generate number from discrete uniform distribution in the interval (a,b+1) we do the following

• Generate a uniform random number u in the interval (0,1)
• pick x from the interval (a,b+1) such that ​
  • That is pick x such that
• here a=40 and b=100, hence we will pick an integer x such that
  • 

the resulting xs are the sales

These are 5 draws for sales

The average sale (expected sales) is