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Binomial Distribution

Definition: 

 The Binomial Distribution is one of the discrete probability distribution. It is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled Successand Failure. The Binomial Distribution is used to obtain the probability of observing r successes in n trials, with the probability of success on a single trial denoted by p.


Formula:

P(X = r) = nCr p r (1-p)n-r
where,
             n = Number of events
             r = Number of successful events.
             p = Probability of success on a single trial.
nCr = ( n! / (n-r)! ) / r!
             1-p = Probability of failure.


Example: Toss a coin for 12 times. What is the probability of getting exactly 7 heads.


Step 1: Here, 
                Number of trials n = 12
                Number of success r = 7 since we define getting a head as success
                Probability of success on any single trial p = 0.5

Step 2: To Calculate nCr formula is used. 
nCr = ( n! / (n-r)! ) / r!
            …

Pigovian tax

Pigovian tax
Pigovian tax (also spelled Pigouvian tax) is a tax levied on a market activity that generatesnegative externalities. The tax is intended to correct the market outcome. In the presence of negative externalities, the social cost of a market activity is not covered by the private cost of the activity. In such a case, the market outcome is not efficient and may lead to over-consumption of the product. A Pigovian tax equal to the negative externality is thought to correct the market outcome back to efficiency. In the presence of positive externalities, i.e., public benefits from a market activity, those who receive the benefit do not pay for it and the market may under-supply the product. Similar logic suggests the creation of Pigovian subsidies to make the users pay for the extra benefit and spur more production. Pigovian taxes are named after economistArthur Pigou who also developed the concept ofeconomic externalitiesWilliam Baumol was instrumental in framing Pigou'…

The Coase theorem

The Coase theorem states that where there is a conflict of property rights, the involved parties can bargain or negotiate terms that are more beneficial to both parties than the outcome of any assigned property rights. The theorem also asserts that in order for this to occur, bargaining must be costless; if there are costs associated with bargaining (such as meetings or enforcement), it will affect the outcome. The Coase theorem shows that where property rights are concerned, involved parties do not necessarily consider how the property rights are granted if they can trade to produce a mutually advantageous outcome.  

This theorem was developed by Ronald Coase when considering the regulation of radio frequencies. He posited that regulating frequencies was not required because stations with the most to gain by broadcasting on a particular frequency would have an incentive to pay other broadcasters not to interfere.

The Coase Theorem: Controlling Externalities through assigning property r…