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a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain the partition of V induced by R.
b) Let A = {1, 2, 3, 4} and define R on P(A) -{Ø} by xRy iff x ∩y ≠Ø. Is R an equivalence relation? Describe
The quotient of 3d 3 and 9d 5 is The key word quotient means division so the problem becomes 1d 3 -5/ 5. Divide the coef?cients: 1d 3 /3d-5 . While dividing like bases, subt
f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
Marginal Probability Probability of event A happening, denoted by P(A), is called single probability, marginal or unconditional probability. Marginal or Uncondi
Find an integrating factor for the linear differential equation and hence Önd its general solution: SOLVE T^ 2 DY DX+T2
Integrals Involving Trig Functions - Integration techniques In this part we are going to come across at quite a few integrals that are including trig functions and few metho
how do you solve expressions
Q. How to calculate Mode? The mode of a data set is the value that is repeated most often in the data set. It has the highest frequency. There can be one, more than one, or n
Find no. of non negative integral solutions x 1 +x 2 +x 3 +4x 4 =20 Solution) 140. Break them into prime factors . Put 4 = 2^2 and every variable will have factors in 2,3,5 with
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Let a = 5200 and b = 1320. (a) If a is the dividend and b is the divisor, determine the quotient q and remainder r. (b) Use the Euclidean Algorithm to find gcd(a; b). (c)
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