Specific statistical methods have helped the civilization to identify, study, and solve a variety of problems. Statistics help people make effective decisions in uncertain situations. Probability is used to illustrate events that do not take place with certainty. Statistics reveals the concepts of association between two variables, probability, random sampling, and estimation.
People in various occupations tend to apply statistics. Health specialists use statistical methods to resolve whether a particular drug or procedure is useful in the treatment of medical issues. Weather forecasters use statistics to more precisely predict the weather.
Engineers use statistics to scale standards for product safety, security and quality. Scientists employ statistical methods to conduct efficient experiments. Economists apply statistical techniques in foreseeing future economic tendencies. Questions in statistics and probability can sometimes be pretty tricky and acquire a lot of time, knowledge and effort. It also sometimes occurs that the assignments do not always correspond with the knowledge and information given to the students within the course.
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With our service you have the possibility to ease your education process and concentrate on more important matters. Common Errors in Calculus Exercises. Probabilities of various events in rolling of dice, or flipping of coins are examples of objectives probability in as much as they are based on dependable evidences.
A probability which is calculated on the basis of personal experience or opinion is called a subjective probability. Probabilities of earning super profits for 10 years are the examples of subjective probability in as much as such probabilities are calculated purely on the basis of personal opinion of some experts. The probability of a dependent event is called a conditional probability. If there are two dependent events, say A and B the conditional probability. If there are two dependent events, say A and B the conditional probability of A given that B has happened is given by ;.
And the conditional probability of B given that A has happened is given by. Which represents that the probability of A, B and C is equal to the probability of A times the probability of B given that A has happened, B times the probability of C given that both A and B have happened.
It is to be noted that where conditional probability is attached to the two independent events say A and B, the conditional probabilities of A and B will be represented thus:. The product of a prior probability and a conditional probability is the joint probability of any two dependent or independent events. The values of joint probabilities of any two events can be better represented through a table known as the Joint Probability Table in which the intersection of the rows and columns are shown as the joint probabilities of the various events.
The following examples would make the point very clear. This is, also, otherwise called as unconditional probability which refers to the probability of occurrence of an event without waiting for the occurrence of another event.
The marginal probability of the events, say, A and B are represented as follows:. In a joint probability table, the marginal probability of an event can be easily calculated by adding the two joint probabilities relating to an event both row and column-wise. It is to be noted that sum of the marginal probabilities of all the related events will be equal to one.
All these have been shown in the joint probability tables as solution to the illustrations 19 and 20 above. Interrelationship between the Conditional, Joint and Marginal Probabilities: All the three Conditional, Joint, and Marginal probabilities are inter-related with each other which can be seen from the following model:.
This probability is known is known is different names, viz. This has been introduced by Thomas Bayes an English mathematician in his work known as Bayesian Decision Theory published in This theory consists of finding the probability of an event by taking into account of a given a sample information.
Thus, a sample of 3 defective items out of event A might be used to estimate the probability that a machine is not working properly event B.
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Probability refers to ‘an event’ the happing and non-happening of which is uncertain, or contingent. Literally, it means a chance, a possibility, likelihood, or an odd. We provide probability homework help. The terms probability and statistics always make sense when used together despite the fact that the two words have different meanings. This owes to the reality that probability is a measure of how likely an event would occur while statistics is a branch of mathematics that permits researchers to .
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