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Find the probability distribution of the random variable X, which can take only the values 1,2,3 given that P(1)=10/30,P(2)=1/3 and P(3)=12/33.


Explain the types of risks in 2008 financial crisis?

iven an integer N  denotes N×N  matrix. Initially, each cell of matrix is empty. U r given K  tasks. In each task, you are given a cell (i,j)  where cell (i,j)  represents

ith  row and jth  column of given matrix.

I/p format

  • first line contains two space-separated integers N and K where N is number of rows and columns in given matrix and K is number of tasks respectively.
  • Next K lines contain two space-separated integers i and j.

O/p format

Print K space-separated integers denoting numberr of empty cells in matrix.


1.Given below is the dissociation of NH3 in water having a Kb value of 1.8 × 10-5. The reaction started with the equilibration of 0.65 M NH3. A common ion that is 0.25 M NH4Cl, was added to the initial solution and waited for some time for the reaction to reach equilibrium once again.

NH3(aq) + H2O(l) ↔ NH4+(aq) + OH-(aq)

Determine the pH of the solution given after the addition of the common ion. The Kw of water is 1.0 × 10-14.


2.What is the pH of a buffer solution that is 0.350 M ethylamine and 0.200 Methylammonium chloride, after the addition of 0.100 M HNO3? The value of Kb for ethylamine is 4.7 x 10-4.

Suppose the market for widgets can be described by the following equations: Demand: P = 10 - Q Supply: P = Q - 4 where P is the price in dollars per unit and Q is the quantity in thousands of units. Then: a. What is the equilibrium price and quantity? [2] b. Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive? [5] c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of $1 per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government? 


Suppose the government wants to limit imports of a certain good. Is it preferable to use an import quota or a tariff? Motivate why you recommend one over the other


Demonstrate how if a public good is to be provided in some fixed amount or not provided at all, then a necessary and sufficient condition for provision to be Pareto efficient is that the sum of the willingnesses to pay (the reservation prices) exceeds the cost of the public good


Demonstrate how if a public good is to be provided in some fixed amount or not provided at all, then a necessary and sufficient condition for provision to be Pareto efficient is that the sum of the willingnesses to pay (the reservation prices) exceeds the cost of the public good


1. Start off by importing the cars.csv file in the jupyter notebook.

2. Generate a line plot graph for the column ‘model’ and ‘hp’.

a. Map the ‘model’ column on the x-axis.

b. Map the ‘hp’ column on the y-axis.

c. Provide the x-axis label as Models of the cars.

d. Provide the y-axis label as Horse-Power of Cars.

e. Set the title as Model Names vs HorsePower. 





How to find the maximum and minimum from the list by using loops


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