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How to find total no. of unordered pairs of disjoint subsets of a finite set? Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into A or B or the set S (3 choices). We only require to exclude the possibility of all elements choosing to be in S itself. Therefore the number of ways is 3n-1
Using R function nlm and your code from Exercise E1.2, write an R function called pois.mix.mle to obtain MLEs of the parameters of the Poisson mixture model.
In a group of 1000 people, there are 750 people will speak English and 400 people will speak Russian. How many may speak English only? How many will speak Russian? How many can spe
Cardioids and Limacons These can be split up into the following three cases. 1. Cardioids: r = a + a cos θ and r = a + a sin θ. These encompass a graph that is vaguel
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
f(x)=sin x+cos x in the interval {0,90}
Velocity Problem : Let's look briefly at the velocity problem. Several calculus books will treat it as its own problem. . In this problem we are given a position function of an
Determine the differential for following. y = t 3 - 4t 2 + 7t Solution Before working any of these we have to first discuss just
States the negation of the statement ∀x ∃y (xy = 1) so that no negation precedes a quantifier. Ans: The negation of the following statement is written as ~ [∀x ∃y (xy = 1)]. An
The probability of a rare disease striking a described population is 0.003. A sample of 10000 was examined. Determine the expected no. suffering from the disease and thus find out
With reference to Fig. 1(a) show that the magnification of an object is given by M=SID/SOD. With reference to Fig. 1(b) show that the size of the penumbra (blur) f is given by f
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