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# Statistics – Variables

Statistics –Variables

1. A random variable can be defined as a function which perhaps relates a real number with each element of the sample space. A random variable could be either discrete or could be continuous.

A continuous random variable is a random variable whose outcomes ofan experiment are uncountable with a continuous sample space. Anexample can be the proportion of my monthly income that I spent onclothing that definitely lies between 0 and 1.

On the other hand, a discrete random variable is a random variable inwhich the outcomes of an experiment are countable and finite orcountable and infinite which takes distinct values. An example can belike the number of students in a statistics class.

1. A binomial experiment has the following features that define it

• The outcomes in each trial are independent of each other

• The probability of the success denoted by P is constant for each test made, and so it calls that the one for failure is also constant.

• The binomial experiment has “n” identical trials.

• The results of each trial can be of the two outcomes, that is, success or failure

Some practicalexamples of binomial experiments include

• The case of ranking students in a statistics exam done at the close of the semester, a student can either pass or fail, and the performance of a given student is independent of the performance of the other student. If one fails the test, it does not tell whether the other student will pass or fail the exam.

• Secondly, in a research question, the number of people who gives NO as an answer is an example of a binomial experiment. The fact that the first person said no will not affect or influence in any way the other person giving no or yes for an answer when his turn comes.

1. Any normal curve exhibits have the following features

• Has its means at the center, and it divides the area into two equal halves

• It is symmetrical about the central values

• The total area under the curve adds to 1 which is perhaps equal to the total probability

• It is defined and obtained by its standard deviation and its mean

• It is probably bell shaped

• In the curve, the median = mean = mode

1. – In the normal curve, the standard deviation gives us how the curve is spread out, that is, it quantifies the dispersion of the values of the observations represented by the curve about the mean.

• On the other hand, the mean divides the area of the curve into two equal halves to give us the positive and negative values of the distribution.

1. – An exponential distribution is one which describes the time between events or activities. Therefore gives the time elapsed between events.

• On the other hand, a Binomial distribution is one that summarizes a cluster of observations that are independent via the number of observations in that group which perhaps stand for one of the outcomes success, otherwise, failure.

• Examples of an exponential distribution include

1. The number of kilometers a motorbike can run before its tyres become worn out

2. The time is taken by the supermarket cashier to serve a customer while waiting in a queue.

• Examples of a binomial distribution include

1. The number of respondents who said yes in a survey experiment

2. The ranking of students in a statistics continuous assessment examination.

References

William, Feller. (1968). Probability theory and its applications

Weiss, N. A. (2016). Introductory Statistics (10th ed.). New York,NY: Pearson Education.

Medhi, T. (1982). Stochastic process

Mark Pinsky, Samuel, K. (2011). An introduction to probabilitymodeling.