6. Suppose we have itms storod in a cal. The case is bidiroctional which means t

Question

6. Suppose we have itms storod in a cal. The case is bidiroctional which means that it can rotate in either direction. The time to complete an entire rotation in one direction is 24 seconds. Of course, when a request arrives, the carousel is rotated in the direction that yields the shorter rotation time. (a) What is a reasonable assumption for the distribution of the rotation time to the pick location? (b) What is the probability density function for this distribution? (c) What is the mean rotation time to a pick location? (d) What is the variance of the rotation time to a pick location?

Explanation / Answer

The time to complete one rotation in one direction = 24 seconds

C. mean rotation time to pick location = np(24)

n= no.of trials = 1

p= event probability = 1/2

mean rotation time = 1/2 * 24= 12 seconds

D. variance of the rotation time = np(1-p) * 24

= 1/2(1-1/2) *24 = 1/4 *24 = 6 seconds

B. Probability Density Function = n!/x!(n-x)! * p^x * (1-p)^n-x

x= no.of events = 1

PDF = 1!/1!(1-1)! * (1/2)^1 (1-1/2)^(1-1)

= 1 * 1/2 * 1 = 1/2 = 0.5

A. reasonal assumption for the distribution of rotation time to pick location is

short distance/ 24 seconds , long distance/ 24 seconds.

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