The pdf used is f(x) = p q^(x-1) , x = 1,2,3,4,... where q=1-p
in finding E(X) we use the binomial series of (1-u) ^(-2)
for E(X^2) we manipulate it into E[X(X-1)] and then use the binomial series for (1-u)^(-3)
mean = 1/p
variance = q/[p^2]
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liquid helium at extremely low temperatures shows properties different from other normal liquids , like creeping out along the sides of the vessel, rising into a fountain and so on.
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Normal orthodox swing of the cricket ball happens when the ball is hard /new. Usually one side of the cricket ball is allowed to be roughened by normal wear and tear during play, and the other side of the cricket ball is usually made shiny by polishing on the trousers. This difference in roughness and the position of the seam is what seems to make the cricket ball swing. Usually the ball will swing towards the rougher side, so that for an outswinger, the rougher side will be on the side of the second or third slip fielders
When the ball has been in use for around 35 overs or more (depending on the conditions of the ground and the ability of the bowler) , the ball might swing towards the shiny side (hence the name reverse swing).
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A nice song about adding fractions set to the tune of mamma mia by abba
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Going green seems to be the buzz word these days. This is the case with the food used by humans in most of the developed countries. The trend seems to be catching up in the case of pet foods as well. But in a country like India , where a lot of people find it hard to have at least one good meal per day, all of this seems to be a bit over the top.
Now truly food for human consumption that is to be labelled as organic must be grown without the use of pesticides and must be processed without using any chemical processes. There are very good regulators in the USA which control these in the case of human food.
But as far as the pet food industry is concerned , the regulations are not so rigid.
If you observe some of the dog food, you might notice the bright colours and artificial flavours, additives, preservatives etc. Some of these may be harmful to the pets and might cause problems like itches / allergies on the skin or ever worse medical problems. Most of the pet food is made from waste meat leftover after high quality portion of the meat has been taken for human consumption. Some of the commercial pet food might contain damaged meat and waste grain that might be mouldy. In short the pet food industry might use most of the waste leftovers from the food used for human consumption.
So your best bet would be to find pet food that might be natural , and does not contain pesticides and fungicides. You could also source the grains that are organically grown for human consumption and then process it for use as pet food. If you truly love your pets, you will enjoy spending the time to process the food grains. But be careful and see if the vitamin and mineral requirements of your pet can be fulfilled by your pet food. Liver , rice , vegetables can make up a good mixture.
If you search around you might also see some certified types of pet food / dog food, or pet food made from all natural ingredients in some pet shops.
Also raw food which is uncooked might have higher quantity of proteins and minerals. But be careful about feeding raw meat or stale food to pets as they might contain toxins harmful to the pets.
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limiting case of the binomial is poisson distribution
If in a binomial distribution B(n ,p) , n is large and p is small and np is finite,then the binomial distribution can be approximated using the Poisson distribution with mean =np.
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