 # Passion Distribution

Passion Distribution It is limiting case of binomial distribution. Let the number of events n is large (n→∞) and probability of success in each experiment is 0 and np = λ (say) . Where r = 0, 1, 2, … And λ = np. Here, λ is know as parameter of Poisson distribution. P (r Read more about Passion Distribution[…] # Some Special Integrals – Problems

Some Special Integrals – Problems . Example 1: is equal to  Solution: Given . . . (cos2x = 2cos²x – 1 and sin2x = 2sinx cosx) . . Let . . . . . Example 2:   is equal to Solution: Given, . . . . … (1) Where . . … (2) Equation (2) Read more about Some Special Integrals – Problems[…] # Condition for Common Roots – Problems

Condition for Common Roots – Problems Condition for Common Roots: Let ax² + bx + c = 0 and px² + qx +r = 0 have a common roots α Then ax² + bx + c = 0 and px² + qx + r = 0 Solving equations . Condition for both roots to be Read more about Condition for Common Roots – Problems[…] # De arrangements

De arrangements If n distinct objects are arranged in a row, then the number of ways in which they can be de arranged so that none of them occupies its original place is. . And it is denoted by D(n) If r(0 ≤ r ≤ n) objects occupy the place assigned to them i.e., their Read more about De arrangements[…] # Global (Absolute) Maxima or Minima

Global (Absolute) Maxima or Minima Global (Absolute) Maxima or Minima in [a, b]: Step 1:  Find out all the critical points of f(x) in (a, b). Let c₁, c₂, …, cn be the different critical points. Step 2: Find the value of the function at these critical points and also at the end points of Read more about Global (Absolute) Maxima or Minima[…] # Addition Theorem of Probability

Addition Theorem of Probability (i) If A and B be any two events in a sample space S, then the probability of occurrence of at least one of the event A and B is given by P(AᴜB) = P(A) + P(B) – P(A∩B) Note: ⇒If A and B are mutually exclusive events, then A∩B = Read more about Addition Theorem of Probability[…] # Test for Local Maximum/ Minimum – Second Derivative Test

Test for Local Maximum/ Minimum – Second Derivative Test Second Derivative Test:  First we find the roots of f’(x) = 0. Suppose x = a is one of the roots of f’(x) = 0 Now, find f’’(x) at x = a (a)If f’’(a) = negative, then f(x) is maximum at x = a. (b) If Read more about Test for Local Maximum/ Minimum – Second Derivative Test[…] # Test for the local Minimum/ Maximum – First Derivative Test

Test for the local Minimum/ Maximum – First Derivative Test Test for the local maximum/ minimum at x = a, if f(x) is differentiable at x = a: If f(x) is differentiable at x = a   and if it is a critical point of the function (i.e., f’(a) = 0), then we have the following Read more about Test for the local Minimum/ Maximum – First Derivative Test[…]