Correlation Coefficient

Introduction:

            Correlation Coefficient also called as Cross Correlation Coefficient. It is used to find the quality of the of least squares fitting to the given data. Calculates of the power of linear connection between two variables. Correlation is forever between -1.0 and +1.0. If the correlation is +ve, we have a +ve relationship If it is -ve, the relationship is -ve. Calculates of the power of linear connection between two variables. Correlation is forever between -1.0 and +1.0. If the correlation is +ve, we have a +ve relationship. If it is -ve, the relationship is -ve.

Correlation Co-efficient Formula:

`"Correlation(r)" =[ NsumXY - ((sumX)(sumY)) / (sqrt([NsumX^2 - (sumX)^2][NsumY^2 - (sumY)^2])]]`

Where              N = Number of values or elements
              X = 1st Score
              Y = 2nd Score
              ` sum` XY = Sum of the product of 1st and 2nd Scores
              `sum` X = Sum of 1st Scores
              `sum` y = Sum of 2nd Scores
              `sum` x² = Sum of square 1st Scores
              `sum` y² = Sum of square 2nd Scores

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Standard frequency distribution and types

Introduction:

A Frequency Distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. Some of the graphs that can be used with frequency distributions are histograms, line graphs, bar charts and pie charts. Frequency distributions are used for both qualitative and quantitative data.

Types of Standard Frequency Distribution:

Different types of standard frequency distribution are,

• Univariate frequency distribution
• Joint frequency distribution tables

Univariate frequency distribution:

                It is a list of values that can be ordered by the quantity. It can show the values for each value appears for number of times.

Joint frequency distribution:

                 It is used as two-way tables. It is also called as bivariate joint frequency distribution.

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Please leave your comments, if you have any doubts.

Expected Value of a Continuous Random Variable

Introduction:

 The expected value is a measure of central location. For example of expected value continuous, your final grade in. this course will be the expected value of your performance in different tasks (quizes, exams, projects,...). The expected return of a lottery is equal to the average gain of that lottery. The expected value of a continuous random variable Y having probability density function f(y) is

               E(Y) = `int``y f(y)`dy

            For continuous random variables, the probability of an individual outcome in R(Y) is not defined, and R(Y) is uncountably infinite.

Expected Value of a Continuous Random Variable:

          The expected value continuous of a random variable Y, is denoted by E(Y) and may be interpreted as the long-term average value of Y. In the case of a discrete random variable, taking values y_1, y₂, y₃...

                E(Y) = EY_j P(Y=y_j)

          The random variable's expected value is average or central value. Here Y is defined as a random variable. If Y is a continuous random variable with probability density function f(y), then the expected value of Y is defined by:

                 µ = E(X)= x f(x) dx

           The expected value continuous or mean of a continuous random variable Y, denoted E(Y) (or, alternatively, µy), is the long run average of the values taken on by the random variable. For some random variables, E (│Y│) = ∞; and we say that the expected value does not exist.

About Conditional Probability

Introduction

     Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Joint probability is the probability of two events in conjunction. That is, it is the probability of both events together. The joint probability of A and B is written or
     Baye's theorem is named after the British mathematician Thomas Bayes who published it in a research paper in 1763. It gives one of the important applications of the conditional probabilities by using the additional information supplied by the experiment or the past records. The updated conditional probability of A, given I and the outcome of the event B, is known as the posterior probability, P(A|B,I).

Conditional Probability

     Let A and B be any two events associated with a random experiment. The probability of occurrence of event A when the event B has already occurred is called the conditional probability of A when B is given and is denoted as P(A/B).