Binomial nomenclature (also called binominal nomenclature or binary nomenclature) is a formal system of naming species of living things by giving each a name composed of two parts, both of which use Latin grammatical forms, although they can be based on words from other languages. Such a name is called a binomial name (which may be shortened to just "binomial"), a binomen or a scientific name; more informally it is also called a Latin name. The first part of the name identifies the genus to which the species belongs; the second part identifies the species within the genus. For example, humans belong to the genus Homo and within this genus to the species Homo sapiens. The formal introduction of this system of naming species is credited to Swedish natural scientist Carl Linnaeus, effectively beginning with his work Species Plantarum in 1753.[1] The application of binomial nomenclature is now governed by various internationally agreed codes of rules, of which the two most important are the International Code of Zoological Nomenclature (ICZN) for animals and the International Code of Nomenclature for algae, fungi, and plants (ICN) for plants. Although the general principles underlying binomial nomenclature are common to these two codes, there are some differences, both in the terminology they use and in their precise rules. In modern usage, the first letter of the first part of the name, the genus, is always capitalized in writing, while that of the second part is not, even when derived from a proper noun such as the name of a person or place. Similarly, both parts are italicized when a binomial name occurs in normal text. Thus the binomial name of the annual phlox (named after botanist Thomas Drummond) is now written as Phlox drummondii. In scientific works, the "authority" for a binomial name is usually given, at least when it is first mentioned, and the date of publication may be specified. In zoology

...CHAP 1 - Binomial Expansions (Kembangan Binomial)
The binomial theorem describes the algebraic expansion of powers of a binomial.
Figure 1 : Example use the binomial Expansion in geometric
There are 3 methods to expand binomial expression
Method 1 - Algebra method
Expansion two or more expression.
Example: The expansion depend on power value (n)
n = 0, (a + x)0 = 1
n = 1, (a + x)1 = a + x
n = 2, (a + x)2 = (a + x) (a + x) = a2 + 2ax + x2
n = 3, (a + x)3 = (a + x) (a + x) (a + x) = a3 + 3a2x + 3ax2 + x3
n = 4, (a + x)4 = (a + x)(a + x)(a + x)(a + x) = a4 +4a3x +6a2x2 +4ax3+ x4
Method 2 - PASCAL Triangle
Pascal's triangle is a triangular array of the binomial coefficients in a triangle. It is named after the French mathematician Blaise Pascal
Base on algebra method.
only using the coefficients of terms.
Power value Coefficient
n = 0 1
n = 1 1 1
n = 2 1 2 1
n = 3 1 3 3 1
n = 4 1 4 6 4 1
n = 5 1 5 10 10 5 1
n = 6 1 ? 1
Example:
(1 + 2x)5
n = 5 1 5 10...

...BINOMIAL THEOREM
OBJECTIVES
Recognize patterns in binomial expansions.
Evaluate a binomial coefficient.
Expand a binomial raised to a power.
Find a particular term in a binomial expansion
Understand the principle of mathematical induction.
Prove statements using mathematical induction.
Definition: BINOMIAL THEOREM
Patterns in Binomial Expansions
A number of patterns, as follows, begin to appear when we write
the binomial expansion of a b n, where n is a positive integer.
a b a b
a b 2 a 2 2ab b 2
a b 3 a3 3a 2b 3ab 2 b3
a b 4 a 4 4a3b 6a 2b2 4ab3 b 4
5
a b a5 5a 4b 10a3b 2 10a 2b3 5ab4 b5
1
and so on.
In each expanded form above, the following can be observed:
n
1. The first term is a , and the exponent on a decreases by 1
in each successive term.
2. The last term is b n and the exponent on b decreases by 1
in each successive term.
3. The sum of the exponents on the variables in any term is
equal to n.
n
n 1 terms in the expanded form of a b .
4. There are
Definition:
Binomial Coefficients
An interesting pattern for the coefficients in the binomial expansion
can be written in the following triangular arrangement
n=0
n=1
n=2
n=3
n=4
n=5
n=6
a bn
1
1
1
1
1
1
1
1
2
3
4...

...BINOMIAL THEOREM :
AKSHAY MISHRA
XI A , K V 2 , GWALIOR
In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc, where the coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in thebinomial expansion are known as binomial coefficients. They are the same as the entries of Pascal's triangle, and can be determined by a simple formula involving factorials. These numbers also arise in combinatorics, where the coefficient of xn−kyk is equal to the number of different combinations of k elements that can be chosen from an n-element set.
HISTORY :
HISTORY This formula and the triangular arrangement of the binomial coefficients are often attributed to Blaise Pascal, who described them in the 17th century, but they were known to many mathematicians who preceded him. The 4th century B.C. Greek mathematician Euclid mentioned the special case of the binomial theorem for exponent 2 as did the 3rd century B.C. Indian mathematician Pingala to higher orders. A more general binomial theorem and the so-called "Pascal's triangle" were known in the 10th-century A.D. to Indian mathematician Halayudha and Persian...

...Four-D? That is, what is the probability of Four-D rejecting a shipment of drives from DataStor?
The probability of Four-D rejecting a shipment of drives from DataStor, if there process is “in control”, is 3.8%.
Four-D conducts the PDQ test on 10 random samples of each shipment.. We used this as the sample size in the Binomial Probability Distribution feature of PhStat.
The probability of the event, that a drive would fall below Four-D’s quality standard of 6.2, was gained from Question 1.
Outcomes 1 – 10 were queried because there are 10 possible scenarios of Four-D rejecting the sample. The cumulative probability of Four-D rejecting a shipment from DataStor’s “in control” process is 3.8%. See the table below for the calculation.
The binomial probability feature was used because this is a decision with two conditions: acceptable or unacceptable.
Binomial Probabilities | | |
| | | |
Data | | |
Sample size | 10 | | |
Probability of an event of interest | 0.0038304 | | |
| | | |
Statistics | | |
Mean | 0.0383038 | | |
Variance | 0.0381571 | | |
Standard deviation | 0.1953384 | | |
| | | |
Binomial Probabilities Table | | |
| X | P(X) | |
| 1 | 0.037 | |
| 2 | 0.00064 | |
| 3 | 6.6E-06 | |
| 4 | 4.4E-08 | |
| 5 | 2E-10 | |
| 6 | 6.5E-13 | |
| 7 | 1.4E-15 | |
| 8 | 2.1E-18 | |
| 9 | 1.8E-21 | |
| 10 |...

...#1 True or false: Even if the sample size is more than 1000, we cannot always use the normal approximation to binomial.
Solution:
If a sample is n>30, we can say that sample size is sufficiently large to assume normal approximation to binomial curve.
Hence the statement is false.
#2
A salesperson goes door-to-door in a residential area to demonstrate the use of a new Household appliance to potential customers. She has found from her years of experience that after demonstration, the probability of purchase (long run average) is 0.30. To perform satisfactory on the job, the salesperson needs at least four orders this week. If she performs 15 demonstrations this week, what is the probability of her being satisfactory? What is the probability of between 4 and 8 (inclusive) orders?
Solution
p=0.30
q=0.70
n=15
k=4
[pic]
Using Megastat we get
| | |15 |
| |0.3 | P |
| | | |
| | |Cumulative |
|k |p(k) |Probability |
|0 |0.00056 |0.00056 |
|1 |0.00503 |0.00559 |
|2 |0.02154 |0.02713 |
|3 |0.05848 |0.08561 |
|4 |0.11278 |0.19838 |
|5 |0.16433 |0.36271 |
|6 |0.18781 |0.55052...

...The binomial theorem is a simplified way of finding the expansion of a binomial to a certain power. We can of course find the expanded form of any binomial to a certain power by writing it and doing each step, but this process can be very time consuming when you get into let’s say a binomial to the 10th power.
Example:
(x+y)^0=1 of course because anything to the power if 0 equal 1
(x+y)^1= x+y anything to a power of 1 is just itself.
(x+y)^2= (x+y)(x+y) NOT x^2+y^2.
So expand (x+y)(x+y)=x^2+xy+yx+y^2 or x^2+2xy+y^2.
(x+y)^3=(x+y)(x+y)(x+y) now expanding it is getting quite long. Of course we could do this using the distribution property, but there must be an easier way of expanding binomials with out doing all the steps that is takes to expand something like (x+y)^10.
As surprising as it might be, there is an easier way of find what a binomial equals to a larger power. Using combinations we can find the coefficients of each term. Lets look at an example. The (x+y)^3 was the one I didn’t finish. Let’s look at it now. Using the equation in combination, we can insert the power that we are using and for each term to find the coefficient of each term.
Ex:
This process can be even easier. Blaise Pascal, a famous French mathematical among other things put together a triangle made up of numbers where each number represents the coefficient of each term (when expanded) in a...

...The Binomial Distribution
October 20, 2010
The Binomial Distribution
Bernoulli Trials
Deﬁnition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure.
1
Tossing a coin and considering heads as success and tails as failure.
The Binomial Distribution
Bernoulli Trials
Deﬁnition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure.
1
Tossing a coin and considering heads as success and tails as failure. Checking items from a production line: success = not defective, failure = defective.
2
The Binomial Distribution
Bernoulli Trials
Deﬁnition A Bernoulli trial is a random experiment in which there are only two possible outcomes - success and failure.
1
Tossing a coin and considering heads as success and tails as failure. Checking items from a production line: success = not defective, failure = defective. Phoning a call centre: success = operator free; failure = no operator free.
2
3
The Binomial Distribution
Bernoulli Random Variables
A Bernoulli random variable X takes the values 0 and 1 and P(X = 1) = p P(X = 0) = 1 − p. It can be easily checked that the mean and variance of a Bernoulli random variable are E (X ) = p V (X ) = p(1 − p).
The Binomial Distribution
Binomial Experiments
Consider the...