Question:

Consider the accompanying second creating capacities. For each situation, distinguish the dissemination included totally. Make certain to indicate the mathematical estimation of all boundaries that recognize the appropriation. For instance, if X is ordinary, give the mathematical estimation of p and a2; if gamma, express an and p. (a) e3r+1612/2

(b) (1 - 30-7 (c) (1 - 20-12 (c0 e3r et

(e) e12/2 (0 (1 - 70-1 (g) e3t+t2/2

Question 30

In leading an analysis in the lab, temperature checks are to be utilized at four intersection focuses in the gear arrangement. These four checks are arbitrarily chosen from a receptacle containing seven such measures. Obscure to the researcher, three of the seven checks give ill-advised temperature readings. Let Xdenote the quantity of deficient checks chose and Y the quantity of nondefective measures chose. The joint thickness for (X, Y) is given in Table 5.5. (a) The qualities given in Table 5.5 can be inferred by understanding that the arbitrary variable Xis hypergeometric. Utilize the consequences of Sec. 3.7 to confirm the qualities given in Table 5.5.

(b) Track down the negligible densities for both X and Y. What kind of irregular variable is Y?

(c) Naturally talking, are X and Y autonomous? Legitimize your answer numerically.

TABLE 5.5

x/y 11 1 2 3 4 0 1/35 1 0 12/35 0 2 0 18/35 0 3 0 4135 0

Question 31

The two most basic kinds of mistakes made by software engineers are sentence structure blunders and blunders in rationale. For a basic language, for example, Fundamental the quantity of such blunders is normally little. Allow X to indicate the quantity of linguistic structure blunders and Y the quantity of mistakes in rationale made on the originally run of an Essential program. Expect that the joint thickness for (X, Y) is as demonstrated in Table 5.6. (a) Discover the likelihood that a haphazardly chosen program will have neither of these kinds of mistakes.

(b) Discover the likelihood that an arbitrarily chosen program will contain in any event one sentence structure blunder and at most one mistake in rationale.

(c) Track down the minimal densities for X and Y. (d) Discover the likelihood that an arbitrarily chosen program contains at any rate two grammar blunders. (e) Discover the likelihood that a haphazardly chosen program contains a couple of blunders in rationale. (f) Are X and Y autonomous?

TABLE 5.6

x/y 0 1 2 3 0 .400 .100 .020 .005 .300 .040 .010 .004 2 .040 .010 .009 .003 3 .009 .008 .007 .003 4 .008 .007 .005 .002 5 .005 .002 .001

Question 32

The joint thickness for (X Y) is given by fxr(x, y) = x3y3116 0 x - s 2, 0 y s 2 (a) Track down the minor densities for X and Y.

(b) Are X and Y free? (c) Discover P[X 5 1].

(d) In the event that it is realized that y = 1, what is FIX 1]? (Try not to utilize any calculation to address this inquiry!

1. Sarah consumes only two goods, which can be divided into fractions: ap ples (:31) and books (.132). Assume the price of books is p2 = 1. Suppose you know that, if she consumes 5 books, she can buy at most 10 apples. And if she consumes 8 books, she can buy at most 4 apples. (3) (b) (C) (d) Determine her income (m) and the price of apples (p1). Write out the equation of her budget line. Draw this on a graph (clearly marking the axes and intercepts) and indicate her budget set. Suppose the government taxes Sarahls apple consumption in the fol- lowing way: for each apple consumed, Sarah must pay a tax of t = %. Write out the equation for her new budget line, and draw it on a graph. After evaluating this policy, the government decides that the tax is too harsh. It now declares that the tax will kick in only after 5 apples. (If 1:1 <_c there is no tax. but if> 5, the tax applies to each apple that exceeds this cutoff.) Sarah will now face a kinked budget line. Write the equations corresponding to each part of her budget line, and draw them on a graph (indicate the bundle at which the kink occurs). This government is extremely indecisive. In another change of policy, it decides that the tax break makes sense for the poor, but there is no reason to oer it to the rich. The new policy is as follows: if a person's income is less than or equal to $10, she gets the tax break (as described in part c), but if her income is greater than $10, she must pay taxes on her entire purchase of apples (as described in part b). Now suppose Sarah's employer offers her a raise of $2. Can we be certain that Sarah will accept the raise? What about a raise of $4? Analyze this by thinking about how the budget set changes after each ralse. 1 Suppose Q units of output can be produced from funits of capital and h units of labour according to the following production function Q = 10KL. (i ) It can be shown that the marginal product of labour is 10K and the marginal product of capital (flour) is 10L. What is the marginal rate of technical substitution when 5 units of labour and 2 units of capital are used? (ii) If the price of labour is $30 per unit and the price of capital is $100 per unit, what is the minimum cost to produce 100 units of the output? What is the quantity of labour and capital used