local central limit theorem

Since a velocity gradient exists across the tube, the mean velocity of the liquid is to be considered. The viscous drag which comes into play when the liquid is in motion, is not taken into account. In above conservation principle, part of K.E. is converted into heat..

Limits of Trigonometric Functions and Sandwich Theorem: for all x in some open interval containing c and suppose Since f is sandwiched between two functions g and h, the above theorem is known as sandwich theorem..

A survey was conducted by a sports channel, about the favorite sport of the people in a locality. Which measure of central tendency is the best for the given situation? => Mode or Median or Range or Mean..

(First Derivative Test) Let f (x) be a real valued differentiable function. Let a be a point on an interval I such that f '(a) = 0. (a) a is a local maxima of the function f (x) if i) f (a) = 0 ii) f (x) changes sign from positive to negative as x increases through a. That is, f (x) > ..

Let f be a differentiable function on an interval I and let a I. Let f "(a) be continuous at a. Then i) 'a' is a point of local maxima if f '(a) = 0 and f "(a) < 0 ii) 'a' is a point of local minima if f '(a) = 0 and f "(a) > 0 iii) The test fails if f '(a) = 0 and f "(a) ..

Evaluation of definite integral by changing limits after suitable substitution. Step I : Let z = g(x) be the desired substitution, dz = g ' (x) dx Step II : when x = a, z = g(a) x = b, z = g(..

Before describing the limits of trigonometric functions, we state few theorems along with Sandwich theorem, which helps in calculating a variety of limits in subsequent chapter..

Probability problems with finite sample spaces Conditional probability Discrete/continuous random variables Mean, variance of discrete random variable Standard distributions Mean, standard deviation of normally distributed random variable Central limit theorem Line..

From the above two theorem, we infer the following (Anti derivative of the function f(x) at b) - (Anti derivative of the function f(x) at a) (ii) The fundamental theorem of integral calculus shows a close relationship between differentiation and integration (iii) These t..

The Normal distribution: Properties of the Normal distribution Using tables of the Normal distribution The Normal distribution as a model for measurements Sampling distributions: Sampling distribution of a sample proportion Sampling distribution of a sample mean Centra..