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Wednesday, October 7, 2009

Binomial distribution

Binomial distribution
pdf (probability distribution function ) of the binomial distribution is
Mean of the binomial distribution = np

Variance of the binomial distribution = npq

mgf (moment generating function of the binomial distribution) is [q + p (e^t) ] ^n

derivation of mean and variance of binomial distribution :derivation of mean and variance of binomial distribution

derivation of mgf of binomial distribution and deduction of mean and variance from the mgf:
mgf of the binomial distribution

derivation of mode of binomial distribution : mode of binomial distribution

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Monday, September 21, 2009

journey from trivandrum to karaikudi

journey from trivandrum to karaikudi

The route was along
Trivandrum - Martandam - Nagercoil - Thirunelveli -Madurai - Melur - Karaikudi
around 400 km. NH 47 and then NH 7

The road from Trivandrum to Nagercoil was the worst in terms of congestion and it took around 2 hours. There was also a small strip of road at Martandam near the bridge which was full of potholes (This could be avoided by taking a side road ).



After that there was a 4-lane road (2-lanes each for either direction) for most of the route to Madurai, which bypassed most of the small towns. But there is some construction going on at some parts of the road. So there is diversion at some parts
and you might also see some vehicles, (some of which are part of the road works ) coming at you from the opposite direction in your lane due to these diversions.
There was also some construction work near Thirunelveli which caused some traffic block for around 20 minutes.



Earlier you would buy sweets like thenkuzhal(the sweet, not the murukku) , aluva etc at thirunelveli. You could buy small cucumbers, pomegranite at various small towns, but most of these are not possible on the new 4-lane road unless you went out of the way along the exit to visit those towns. You could go to the new bus stand at Thirunelveli and buy the sweets from the shops inside the bus stand.

Earlier it was a headache to go through Madurai due to the traffic, but now there is a bypass [ There is a right angle turn towards the right with a (unmarked ?)bump leading to the bypass ] There is a toll of Rs. 35 /-(depending on where you are going) and around four toll gates where you have to show your receipt. There is also some traffic on the bypass since it is connected to the city at some points.



After that the journey is along the 4-lane road for some more distance. You can bypass Melur and take the cut for Karaikudi from the 4-lane road if you know the correct cut [ a vendor of tender coconuts on the roadside told me about that in terms of the approximate distance km ]

After that the road is the usual 2-lane(1-lane each for either direction)with some tamarind trees on the sides.




There is a lot more traffic in Karaikudi. Traffic signals have been installed. A traffic warden shouts at people who have not parked properly through a public address system. Road dividers have come up on the main road.





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Tuesday, September 8, 2009

finance

There seems to be a type of people who live on credit. They buy the latest items like the newest model cars, tv' s etc and do not care if they are not able to afford the items. They would just charge it to their cards or take out a new loan. This was not common in India in the 70's . But with the advent of liberalisation and entry of foreign banks, this type of people are becoming common in india, especially among those in the IT field.
Till the recent recession in the USA and the corresponding slowdown in India, banks were competing with each other in issuing credit cards. Some people would just use a credit card to waste money on the latest and costliest stuff and would then just go about paying the minimum possible on their credit card debt per month.Some people do not even understand that even a single mistake on their part or a late/ missed payment might sometimes just blow up the interest rates on their credit card debt. They sometimes fail to understand that there is no such thing as a free lunch with regard to credit card companies.
Some of the younger generation seem to have forgotten the value of frugality and the concept of living within their means.
When you use credit cards , you do not have the same feeling / care as when you count out currency notes. Also some credit card companies entice you with offers of cash back offers, free gifts etc if you buy a lot of items using your credit card. All of this sometimes leads to overspending.

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Monday, August 3, 2009

collection of problems in integration, differentiation, areas, volumes, trigonometry, matrices, limits

Calculus
problems on integration ------------------------ integration

problems on application of integration like
area, volume, arc length etc ------------------------integration application

problems on differential equations ------differential equation

problems on differentiation------------------------ differentiation

problems on limits ------------------limits

problems on matrices --------------matrices

problems on trigonometry ------trigonometry



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Wednesday, July 29, 2009

cars, bikes etc in india

some links to websites with information / review on used cars, new cars , bike review in india,like maruti 800, maruti alto, ambassador, hyundai santro, cielo, tata nano, tata indica, karizma, bajaj pulsar, ford fiesta, honda city etc

Interesting information on bikes seems to be available at bikeadvice.in
The website seems to be in the form of a blog . Information on carburetor tuning, engine oils etc is available. review/information on some bikes from yamaha , karizma, suzuki , honda , bajaj pulsar etc seem to be available

Another website with review on cars bikes / two wheelers etc is gaadi.com.
Information on price of new cars, as well as of used cars seems to be available.

some other websites with information on new and used cars are

automobileindia.com

cardekho.com

carazoo.com

carwale.com


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.

finding area using green's theorem

The area enclosed by a plane curve C can be evaluated using the following integral

for the proof refer the following page





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Dot Plots, Histograms and Stem-and-Leaf Plots | AP Statistics

  DOT PLOTS, HISTOGRAMS AND STEM-AND-LEAF PLOTS IN AP STATISTICS How to Read, Interpret and Compare Distributions: The Pile–Slice–Say Method...