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Toss a fair coin thrice. Let x denote the number of tails. Find Var(x)
A factory produces a closed rectangular parallelepiped vats having the capacity of 10 cubic meters. Find the dimensions that will make the cost of the lining a minimum?
State the Fubini’s Theorem for the Triple Integrals and list all six possible order of
integration
1. Evaluate (𝑥 − 3) 𝑑 where = , , − 1 ≤ ≤ 1, 0 ≤ ≤ 2, 0 ≤ ≤ 1 }.
There are three kinds of people on an island: knights who always tell the truth, knaves who always lie, and spies who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of other two is. A says “I am the knight,” B says “A is not the knave,” and C says “B is not the knave". Is there a unique solution to determine the knight, the knave, and the spy? If yes, determine who the knight, knave, and spy are.
Two duopolists produce and quantities of a homogenous product . The market demand of the product is given by Q= 240-2p where Q= Qa +Qb and the price of the product. The total functions of the duopolists are given by: C(Qa)= 60+4Qa and C(Qb)= 50+0.625Qb^2
a) Find the level of output that maximizes the profit of each firm and the corresponding profit
and price.
b) Find the level of output that maximizes their profit if the two firms corporate and the
corresponding profit and price.
Two duopolists produce and quantities of a homogenous product . The market demand of the product is given by Q= 240-2p where Q= Qa +Qb and the price of the product. The total functions of the duopolists are given by: C(Qa)= 60+4Qa and C(Qb)= 50+0.625Qb^2
a) Find the level of output that maximizes the profit of each firm and the corresponding profit
and price.
b) Find the level of output that maximizes their profit if the two firms corporate and the
corresponding profit and price
If three coins are tossed, what are the mean, variance, and standard deviation of the number of heads that occur?
A box contains 5 balls. One is numbered 1, two are numbered 2, and two are numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the standard deviation of the numbers on the balls.
A box contains 5 balls. One is numbered 1, two are numbered 2, and two are numbered 3. The balls are mixed and one is selected at random. After a ball is selected, its number is recorded. Then it is replaced. If the experiment is repeated many times, find the standard deviation of the numbers on the balls
