understanding 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..

Limitation of the measuring instrument is an important factor. This leads to uncertainty in measurement. In order to understand this, let us assume that we want to measure the volume of the liquid with a graduated cylinder. If the volume of the liquid is more than 23 mL and les..

Let f be a continuous non-negative function defined on a closed interval [a, b]. Since the value of the function is non-negative, the graph of the function is a curve above X-axis. Let the graph of the curve be as shown in the figure.Let f be a continuous non-negative function defined on a closed i..

The first law of thermodynamics is concerned with the conversion of energy from one form to another. It helps us to understand energy transformation in different chemical reactions. The basic point of the first law is that all physical and chemical processes take place in such a manner th..

The fundamental theorem of calculus is the statement that the two central operations of calculus, differentiation and integration, are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieve..

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..

: 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 Central Limit Theorem Sampling dis..