independent variables

Conclusion - In this chapter we have studied the method of evaluating probabilities of events relating to independent events and conditional events. We have also studied about random variables and their probability distributions, namely binomial distribution and Poisson distribu..

Integration by Parts - Let u and v be two differentiable function of a single independent variable x. Integrating w.r.t x on both sides Let u = f(x), Then \ (1) can be written ..

> as x tends to 'a' through values greater than 'a', then l 2 is called the right hand limit. Differentiation The derivative, measures the rate at which the dependent variable changes with respect to the independent variable. It is one of the most important ideas in Ca..

A first-order differential equation is said to be linear if, in it, the unknown function y and its derivative y' appear with non-negative integral index not greater than one and not as product yy' either. Hence, a first-order linear differential equation is of the form: where p and q are given r..

1. If x is a discrete random variable assuming the values x 1 , x 2 , x 3 ,.,x n with probabilities p 1 , p 2 , p 3 ,., p n respectively then (x 1 ,p 1 ), (x 2 , p 2 ),(x n , p n ) defines a probability distribution of X. 2. Let n independent bernoulli trials be pe..

; p-values; one and two-sided tests; concepts of Type I and Type II errors; concept of power Large sample test for a proportion Large sample test for a difference between two proportions Test for a mean Test for a difference between two means (unpaired and paired) Chi-square test for goodness of fi..

Results and observations of scientific experiments should be properly recorded under headed columns and numbered rows. The headings must include the units in which each quantity is measured. Graphs are very helpful in comparing measurements. The general rule in plotting the graph of a given data ..