In 2022, the JEE Main exam will be conducted in four sessions. As far as the JEE Main exam is concerned, statistics is a topic of great importance. Students can easily score from this topic if learned properly. So they are recommended to learn the equations and tricks in statistics so that they can easily crack the problems from this topic. Statistics is a branch of Mathematics that deals with the analysis, collection, organization, and presentation of data.
In statistics, we use numerical measures of some type of correlation. Thecorrelation coefficient is used to measure the relationship between two variables. It is a statistical concept that helps in finding the relation between predicted and actual values obtained in a statistical experiment. The calculated value denotes the exactness between the predicted and actual values. Its value lies between -1 and +1. If the calculated value is greater than zero, then there is a similar and identical relation between the two variables; otherwise, it shows the dissimilarity between the two variables.
The covariance of two variables divided by the product of their standard deviations gives Pearson’s correlation coefficient. We use the symbol ρ (rho) to denote it.
ρ(X, Y) = cov (X, Y) / σX.σY,
where cov is the covariance. σX denotes the standard deviation of X and σY denotes the standard deviation of Y. We can also express ρ (X, Y) in terms of means and expectations. If E denotes the expectation, μx and μy denotes the mean of x and mean of y respectively, then
ρ(X, Y) = E(X – μx)(Y – μy)/σX.σY
Following are some properties of ρ(X, Y).
1) It remains in the same measurement as in which the two variables are.
2) The sign of ρ(X, Y) will be the same as the variance.
3) The numerical value will lie between -1 and + 1.
4) When ρ(X, Y) approaches zero, it shows a weak correlation.
5) When we interchange the two variables, ρ(X, Y) is not affected.
6) If the value of the coefficient is less than zero, then the correlation is strong and negative. If the value of the coefficient is greater than zero, then the relationship is strong and positive.
A number that can be expressed in the form of p + iq, where p represents the real part, q is the imaginary part is called a complex number, and i is the imaginary unit. It is defined as the square root of -1. We can also denote i as the solution of x2 = -1. Students can expect 2-3 questions from the complex number for any entrance exam. Sothe representation of a complex number is very important while learning this topic. If z = p+iq is a complex number, then the conjugate is given by p-iq. The modulus of z is given by the square root of the sum of squares of the real part (p) and imaginary part (q).
Visit BYJU’S to learn more about complex number and solutions of previous years’ questions on the complex number.