0
You can find the coefficients of an expanded binomial using the numbers in Pascal's triangle. 1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1 These are a few rows of Pascals triangle. Now let's look at a few binomials, expanded to the second and third powers. (a+b)2=a2 +2(ab) + b2 notice the coefficients are the numbers in the second row of the triangle above. (a+b)3= a3+3(a2b)+3(ab2)+b3 and once again note that the coefficients are the numberin the third line of Pascal's triangle. The first line, by the way, which is 1,1 is the coefficient of (a+b)1 This will work for any power of the binomial. There are generalized form for non-integer powers.
Add your answer:
Earn +20 pts
Why is binomial distribution important?
Binomial distribution is the basis for the binomial test of statistical significance. It is frequently used to model the number of successes in a sequence of yes or no experiments.
Which 2 categories are used for binomial nomenclature?
genus and species
What is the symbol for probability of success in a binomial trial?
The symbol for probability of success in a binomial trial is the letter p. It is the symbol used for probability in all statistical testing.
What is the difference between poisson and binomial distribution?
Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution. Binomial is the most preliminary distribution to encounter probability and statistical problems. On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.
What is she binomial probability distribution is used with?
It is used when repeated trials are carried out , in which there are only two outcomes (success and failure) and the probability of success is a constant and is independent of the outcomes in other trials.
In what situation can we use pascals triangle?
pascals triangle is used to solve math problems that have chance of 2 different outcomes, such as flipping a coin
What is the purpose of Pascal's triangle?
The Pascal's triangle is used partly to determine the coefficients of a binomial expression. It is also used to find the number of combinations taken n at a time of m things .
What is the pascals triangle used for?
AnswerPascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician Blaise Pascal. It is mainly used in probability and algebra.1 Row 01 1 Row 11 2 1 Row 21 3 3 1 Row 31 4 6 4 1 Row 4 etc.Each number in the triangle is the sum of the two directly above it. The value of a row, if each entry is considered a decimal place, is a power of 11. So, in row 2, '1,2,1' becomes 112, and '1,5,10,10,5,1' (which will be in row 5) becomes, after carrying , 161,051 which is 115.
How do you convert pascals to centigrade?
You don't. Pascals is used to measure pressure, centigrade is used to measure temperature. Those two are completely different things.
How did Blaise Pascal discover pascals triangle?
He read about it. The idea existed long before Pascal Pierre Raymond de Montmort, just named it after Pascal after Pascal used it to solve problems of probability theory.
What is pascal machine?
Pascal's triangle is used in the expansion of a binomial raised to a power: y = (x - 8)6 ---------------1--------------- -------------1 - 1------------- -----------1 - 2 - 1----------- ---------1 - 3 - 3 - 1--------- -------1 - 4 - 6 - 4 - 1------- ---1 - 5 - 10 - 10 - 5 - 1---- 1 - 6 - 15 - 20 - 15 - 6 - 1-
What is a two word naming system used to name various species?
Usually the genus and species names are used to identify different organisms.
Why is binomial distribution important?
Binomial distribution is the basis for the binomial test of statistical significance. It is frequently used to model the number of successes in a sequence of yes or no experiments.
To correctly write the binomial nomenclature for a particular animal?
A binomial nomenclature is the two name system of naming living things used in classification. The currently used binomial nomenclature was developed by Linneus.
What to Taxons are used in binomial nomenclature?
species and genus are the two categories used during binomial naming of an organism.
Can the chi-square test be used for how well a binomial fits?
Yes, the chi-square test can be used to test how well a binomial fits, provided the observations are independent of one another and all from the same (or identical) binomial distribution.
The currently used binomial nomenclature was developed by?
Linnaeus
