Mr. Smart wants to estimate the demands in 2 separate markets. In the past five

Question

Mr. Smart wants to estimate the demands in 2 separate markets. In the past five years, the demand data of market 1 and 2 are {80, 90, 100, 110, 120} and (60, 80, 100, 120, 140} respectively (data points are not ordered according to time). Mr. Smart aims to know the probability of the future demand in each market being the worst case and the best case. The worst case means demand lessthanorequalto 80 and the best case means demand greaterthanorequalto 120. You may assume that the demand is a discrete or a continuous random variable. How can you find out the probabilities based on the historical data? Which market demand would you prefer and why?

Explanation / Answer

Given, two data sets

market 1 data is (80,90,100,110,120)

market 2 data is (60,80,100,120,140)

each data point has a probability of 0.2 i.e, (1/5)

to find, probabilities

P(X<=80) and P(X>=120) in both the markets

Market 1

worst case

P(X<=80)=P(X<80)+P(X=80)

P(X<=80)=0+1/5

P(X<=80)=0.2

best case

P(X>=120)=P(X>120)+P(x=120)

P(X>=120)=0+1/5

P(X>=120)=0.2

Market 2

worst case

P(X<=80)= P(X<80)+P(X=80)

P(X<=80)=1+1/5

P(X<=80)=0.4

best case

P(X>=120)=P(X>120)+P(x=120)

P(X>=120)=1+1/5

P(X>=120)=0.4

I would choose market 2 data over market 1 as it includes maximum range of values required for the probability

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