binomial nomenclature

Examples of binomial nomenclature in the following topics:

• Classification of Microorganisms

  • Microorganisms are scientifically recognized using a binomial nomenclature using two words that refer to the genus and the species.

• Nomenclature

  • The ether functional group does not have a characteristic IUPAC nomenclature suffix, so it is necessary to designate it as a substituent.
  • Examples of ether nomenclature are provided on the left.

• Naming Organic Compounds

  • A rational nomenclature system should do at least two things.
  • The IUPAC nomenclature system is a set of logical rules devised and used by organic chemists to circumvent problems caused by arbitrary nomenclature.
  • An excellent presentation of organic nomenclature is provided on a Nomenclature Page created by Dave Woodcock.
  • Click on the following link (http://people.ouc.bc.ca/woodcock/nomenclature/index.htm).
  • Click on the following link (http://www.acdlabs.com/iupac/nomenclature/).

• Binomial Expansions and Pascal's Triangle

  • The binomial theorem, which uses Pascal's triangles to determine coefficients, describes the algebraic expansion of powers of a binomial.
  • The binomial theorem is an algebraic method of expanding a binomial expression.
  • This formula is referred to as the Binomial Formula.
  • Applying these numbers to the binomial expansion, we have:
  • Use the Binomial Formula and Pascal's Triangle to expand a binomial raised to a power and find the coefficients of a binomial expansion

• Mean, Variance, and Standard Deviation of the Binomial Distribution

  • In this section, we'll examine the mean, variance, and standard deviation of the binomial distribution.
  • The easiest way to understand the mean, variance, and standard deviation of the binomial distribution is to use a real life example.
  • In general, the mean of a binomial distribution with parameters $N$ (the number of trials) and $p$ (the probability of success for each trial) is:
  • $s^2 = Np(1-p)$, where $s^2$ is the variance of the binomial distribution.
  • Coin flip experiments are a great way to understand the properties of binomial distributions.

• Additional Properties of the Binomial Distribution

  • In this section, we'll look at the median, mode, and covariance of the binomial distribution.
  • There are also conditional binomials.
  • The binomial distribution is a special case of the Poisson binomial distribution, which is a sum of n independent non-identical Bernoulli trials Bern(pi).
  • This formula is for calculating the mode of a binomial distribution.
  • This summarizes how to find the mode of a binomial distribution.

• Nomenclature of Carboxylic Acids

  • In the IUPAC system of nomenclature the carboxyl carbon is designated #1, and other substituents are located and named accordingly.
  • The characteristic IUPAC suffix for a carboxyl group is "oic acid", and care must be taken not to confuse this systematic nomenclature with the similar common system.
  • These two nomenclatures are illustrated in the following table, along with their melting and boiling points.
  • If you are uncertain about the IUPAC rules for nomenclature you should review them now.
  • Some examples of both nomenclatures are provided below.

• Binomial Expansion and Factorial Notation

  • The binomial theorem describes the algebraic expansion of powers of a binomial.
  • Recall that the binomial theorem is an algebraic method of expanding a binomial that is raised to a certain power, such as $(4x+y)^7$.
  • The coefficients that appear in the binomial expansion are called binomial coefficients.
  • The coefficient of a term $x^{n−k}y^k$ in a binomial expansion can be calculated using the combination formula.
  • Use factorial notation to find the coefficients of a binomial expansion

• Alcohol Nomenclature

  • In the IUPAC system of nomenclature, functional groups are normally designated in one of two ways.
  • If you are uncertain about the IUPAC rules for nomenclature you should review them now.
  • Other examples of IUPAC nomenclature are shown below, together with the common names often used for some of the simpler compounds.
  • When the hydroxyl functional group is present together with a function of higher nomenclature priority, it must be cited and located by the prefix hydroxy and an appropriate number.

• The normal approximation breaks down on small intervals

  • Caution: The normal approximation may fail on small intervals The normal approximation to the binomial distribution tends to perform poorly when estimating the probability of a small range of counts, even when the conditions are met.
  • However, we would find that the binomial solution and the normal approximation notably differ:
  • We can identify the cause of this discrepancy using Figure 3.19, which shows the areas representing the binomial probability (outlined) and normal approximation (shaded).
  • TIP: Improving the accuracy of the normal approximation to the binomial distribution
  • The outlined area represents the exact binomial probability.