Poisson Distribution as a Limiting Form of the Binomial Distribution
We shall now deduce the Poisson distribution from the binomial distribution by assuming that n and p 0 such that the product np always remains finite, say l . We shall now use a very important result of limits in Calcu..
We shall now deduce the Poisson distribution from the binomial distribution by assuming that n and p 0 such that the product np always remains finite, say l . We shall now use a very important result of limits in Calcu..Binomial Theorem Summary
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficie..
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficie..Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method)
We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the factors, we get the term a n..
Select the correct statement(s):I. A binomial experiment has only 2 tr..
Select the correct statement(s): I. A binomial experiment has only 2 trials. II. The sum of the probabilities of all outcomes in a probability distribution is 1. III. Testing by administering a drug on 100 patients to determine whether it is effective or not is a binomial..
h) Abiotic and biotic factors
Abiotic factors like temperature, wind, humidity, rainfall, intensity of light has its effect on the density of population. Biotic factors like organisms of other species living in the same area affect the population, as they involve in different types of food relationships. Fo..
Methods of Factorisation
(i) Common factors (ii) By expressing as difference of squares (iii) By grouping (iv) Trinomials (v) Sum or difference of cub..
Partial fractions
Any proper rational function can be expressed as sum of rational fractions, each having a factor of Q(x). Each such fraction is known as Partial fracti..
Any proper rational function can be expressed as sum of rational fractions, each having a factor of Q(x). Each such fraction is known as Partial fracti..Some Observations
For n N, in the expansion of (a + b) n , we observe that: the number of terms is n+1 the exponent of 'a' decreases from n to 0 the exponent of 'b' increases from 0 to n the sum of exponents of 'a' and 'b' in any term is n. the coefficient of any term is n C k where k is..
For n N, in the expansion of (a + b) n , we observe that: the number of terms is n+1 the exponent of 'a' decreases from n to 0 the exponent of 'b' increases from 0 to n the sum of exponents of 'a' and 'b' in any term is n. the coefficient of any term is n C k where k is..Online Algebra Help - Easy, affordable and fun
/content/math/number-theory/polynomials/polynomialsindex.php'>polynomials as the product of two or more polynomials is called factorisation. If A = B x C, B and C are called factors of A. Methods of Factorisation: (i) Common factors (ii) By expressing as difference of squares (i..
Algebra II
Absolute value to solve equations/inequalities Systems of linear equations/inequalities Operations on polynomials Factoring polynomials/trinomials Operations on complex numbers Operations on rational expressions Graphing quadratic equations Quadratic equations in complex number s..
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