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Showing posts from November, 2015

6 - probability

Probability is one the mathematical theories which finds enormous usage in normal world. When you meet your colleague in a mall on a holiday by chance, it could be a rare event of low probability. When we go for a planned medical procedure, we ask the doctor how much risk is involved in it. Depending on the answer, we go for it immediately or postpone a bit . We inherit many traits from our parents. Every human being has 23 pairs(46) of chromosomes. Out of 23 pair of chromosomes of mother, we get 23 (one from every pair);Out of 23 pair of our father we inherit 23.Which one we get from the pair ? Two of them are having equal probability to be inherited.So probability comes into picture when we talk about genetic aspects like your ear appearance  ( genetics ) or hereditary diseases. Quantum mechanics,following uncertainty principle, describes particles position and speed based on probabilistic wave function.This theory, got rejected wrongly by Einstein as he said 'God doesn

5:Continuous compounding formulas and Euler's number

Let see compounding interest formulas.  If P is principal r is interest rate per annum (for 10% interest, r = 0.1)   interest for one year = principal *interest rate = P*r . Total amount after one year =Principal + interest =P+Pr. In annually compound interest rate regime P+Pr = P(1+r) become principal at the end of first year.  Then the next year interest would be calculated on this principal P(1+r) r would be interest for the second year. At the end of second year, total amount would be = P(1+r)+P(1+r) * r = P(1+r)^2 After n years total amount = P(1+r)^n For the same interest rate r, after 6 months how much interest would have been accumulated? Half of the annual interest , that is Pr/2    If interest is compounded to principal semi-annually, at the end of first 6 months Total amont= P+Pr/2=P(1+r/2). For the next 6 months interest will be calculated on this. Interest =P(1+r/2)* r/2. Total amount at the end of one year =P(1+r/2) +(P(1+