A production machine could be assigned the states “operating” and “breakdown”. The transition probabilities reflecting the probabilities of a machine’s either breaking down or operating in the next day is shown in the table below: Day one Day two Operating Breakdown Operating 0.90 0.10 Breakdown 0.70 0.30 Given that the machine is initially operating, determine the probability that it is working in fourth day. Determine the steady state probabilities for each state of the machine.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
- A production machine could be assigned the states “operating” and “breakdown”. The transition probabilities reflecting the probabilities of a machine’s either breaking down or operating in the next day is shown in the table below:
|
Day one |
Day two |
|
|
|
Operating |
Breakdown |
|
Operating |
0.90 |
0.10 |
|
Breakdown |
0.70 |
0.30 |
- Given that the machine is initially operating, determine the probability that it is working in fourth day.
- Determine the steady state probabilities for each state of the machine.
- COVID Ventures Limited manufactures and sells two interdependent drugs, namely, COVID-1 and COVID-2. The demand
functions for the drugs are given by and where P1 is the unit price of COVID-1 and P2 is the unit price of COVID-2, x and y are the number of units in millions sold for COVID-1 and COVID-2 respectively. The total cost of producing both products is given by the function .
Required
- i) Derive the total revenue and total profit functions for COVID Ventures Limited
- ii) Determine the number of units of each drug required to maximize the profit.
iii) Compute the maximum profit.
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