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A two-element series circuit has voltage V 240 08 V and current I 50 608 A. Determine the current which results when the resistance is reduced to (a) 30 percent, (b) 60 percent, of its former value.

(a) Determine whether X and Y are independent, (b) Find P(X P(X Y 1 ). 2

1. Identify the proper scale for each of the following measures: LOC McCabe s cyclomatic number Average depth of nesting Maximum depth of nesting 2. Show that the temperature scales of Celsius and Fahrenheit are an interval scale using the Celsius temperatures of 20, 30, and 40 degrees. 3. Show that McCabe s cyclomatic number satis es the representational theory of measurement. 4. Show that McCabe s cyclomatic number is an interval scale measure. 5. Calculate McCabe s cyclomatic number on the following source code. Draw a control ow graph. Label the regions with Roman numerals. read x,y,z; type = scalene ; if (x == y or x == z or y == z) type = isosceles ; if (x == y and x == z) type = equilateral ; if (x >= y+z or y >= x+z or z >= x+y) type = not a triangle ; if (x <= 0 or y <= 0 or| z <= 0) type = bad inputs ; print type;

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1 2 ).

240 08 56:8 4:22 80:28

1 2,

70:98

1 3 ).

2.93. Let X and Y be identically distributed independent random variables having density function f (u) (2p) 1> 2e u2> 2, ` u `. Find the density function of Z X 2 Y 2.

240 08 54:5 4:40 70:98

2.94. The joint probability function for the random variables X and Y is given in Table 2-9. (a) Find the marginal probability functions of X and Y. (b) Find P(l X 3, Y 1). (c) Determine whether X and Y are independent. Table 2-9

1 Explain why the height example satis es the criteria for valid metrics Criteria 1: Di erent people can be di erent heights Criteria 2: Any two people that we feel are related in height, their numerical heights would agree Criteria 3: Each additional height on a person matches the increase in numerical height Criteria 4: Di erent people can be the same height 2 A study of grade school children found a high correlation between shoe size and reading ability Does this mean that shoe size is a good measure of intelligence No, shoe size correlates well with age Age correlates well with reading ability Neither would be a good measure, since neither would satisfy the representation condition 3 Explain why is money a ratio scale measure and not just an interval scale Money has a well-understood notion of zero.

V 100 08 7:91 Zeq 12:65 18:438

X 0 1 2

2.95. Suppose that the joint probability function of random variables X and Y is given by f (x, y) e cxy 0 0 x 2, 0 otherwise y x

Evaluate the impedance Z1 in the circuit of Fig. 9-19.

(a) Determine whether X and Y are independent. (b) Find P(1 2 P( 1 2 X 1, Y 1).

CHAP. 9]

0. Prove that the density function of X g(u) u!

2.97. A stick of length L is to be broken into two parts. What is the probability that one part will have a length of more than double the other State clearly what assumptions would you have made. Discuss whether you believe these assumptions are realistic and how you might improve them if they are not. 2.98. A floor is made up of squares of side l. A needle of length a l is to be tossed onto the floor. Prove that the probability of the needle intersecting at least one side is equal to a(4l a)>pl 2. 2.99. For a needle of given length, what should be the side of a square in Problem 2.98 so that the probability of intersection is a maximum Explain your answer. 2.100. Let f (x, y, z) e 24xy 2z 3 0 0 x 1, 0 otherwise y 1, 0 z 1

Fig. 9-18

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