Theory of Expectation :: Problems on Profits, Business : Probability Distribution

Solution

Let "x", "y" indicate the profit made by the two firms "A" and "B" respectively. Profit earned = Selling Price − Purchase Price = Selling Price − Rs. 75,000 For "Firm A" The profits that can be made by the firm would be − Rs. 15,000 if it can sell at Rs. 60,000 [60,000 − 75,000] − Rs. 5,000 if it can sell at Rs. 70,000 [70,000 − 75,000] + Rs. 5,000 if it can sell at Rs. 80,000 [80,000 − 75,000] + Rs. 15,000 if it can sell at Rs. 90,000 [90,000 − 75,000] ⇒ The values carried by the variable ("x") would be either       − 15,000 or − 5,000 or + 5,000 or + 15,000 ⇒ "X" is a discrete random variable with       range = {− 15,000, − 5,000, + 5,000, + 15,000} "X" represents the random variable and P(X = x) represents the probability that the value within the range of the random variable is a specified value of "x" Probability that the firm would be able to sell at Rs. 60,000 ⇒ P(60,000) = 0.4 Rs. 70,000 ⇒ P(70,000) = 0.3 Rs. 80,000 ⇒ P(80,000) = 0.2 Rs. 90,000 ⇒ P(90,000) = 0.1 Probability that the profit earned by the firm would be − Rs. 15,000 ⇒ P(X = − 15,000) = P (60,000) = 0.4 − Rs. 5,000 ⇒ P(X = − 5,000) = P (70,000) = 0.3 + Rs. 5,000   ⇒ P(X = + 5,000) = P (80,000) = 0.2 + Rs. 15,000   ⇒ P(X = + 15,000) = P (90,000) = 0.1 The probabilty distribution of "x" would be x − 15,000 − 5,000 + 5,000 + 15,000 P(X = x) or P 0.4 0.3 0.2 0.1 Calculations for Mean x P Px − 15,000 0.4 − 6,000 − 5,000 0.3 − 1,500 + 5,000 0.2 + 1,000 + 15,000 0.1 + 1,500 Total 1 − 5,000 The firms expected profit would be ⇒ Expectation of "x" ⇒ E (x) = Σ px = − 5,000 The firm could expect to make a loss of Rs. 5,000 For "Firm B" The profits that can be made by the firm would be − Rs. 15,000 if it can sell at Rs. 60,000 [60,000 − 75,000] − Rs. 5,000 if it can sell at Rs. 70,000 [70,000 − 75,000] + Rs. 5,000 if it can sell at Rs. 80,000 [80,000 − 75,000] + Rs. 15,000 if it can sell at Rs. 90,000 [90,000 − 75,000] ⇒ The values carried by the variable ("y") would be either       − 15,000 or − 5,000 or + 5,000 or + 15,000 ⇒ "Y" is a discrete random variable with       range = {− 15,000, − 5,000, + 5,000, + 15,000} "Y" represents the random variable and P(Y = y) represents the probability that the value within the range of the random variable is a specified value of "y" Probability that the firm would be able to sell at Rs. 60,000 ⇒ P(60,000) = 0.1 Rs. 70,000 ⇒ P(70,000) = 0.2 Rs. 80,000 ⇒ P(80,000) = 0.5 Rs. 90,000 ⇒ P(90,000) = 0.2 Probability that the profit earned by the firm would be − Rs. 15,000 ⇒ P(Y = − 15,000) = P (60,000) = 0.1 − Rs. 5,000 ⇒ P(Y = − 5,000) = P (70,000) = 0.2 + Rs. 5,000   ⇒ P(Y = + 5,000) = P (80,000) = 0.5 + Rs. 15,000   ⇒ P(Y = + 15,000) = P (90,000) = 0.2 The probabilty distribution of "y" would be x − 15,000 − 5,000 + 5,000 + 15,000 P(Y = y) or P 0.1 0.2 0.5 0.2 Calculations for Mean y P Py − 15,000 0.1 − 1,500 − 5,000 0.2 − 1,000 + 5,000 0.5 + 2,500 + 15,000 0.2 + 3,000 Total 1 + 3,000 The firms expected profit would be ⇒ Expectation of "y" ⇒ E (y) = Σ py = + 3,000 The firm could expect to make a profit of Rs. 3,000