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where y is (n 1), X is (n p), is (p 1), is (n 1), and p k 1. We would like to determine if the subset of regressor variables x1, x2, . . . , xr (r k) as a whole contributes significantly to the regression model. Let the vector of regression coefficients be partitioned as follows: c where

(12-26)

27. In step 1 of the PKZIP attack, as specified beginning on page 114, we explain how t o recover Zi-1 given 2,.Give precise equations for (zi-1)02 3 , ( i 1 2 ... z - ) 4 and ( ~ 2 - 1 ) 3 0 . . , 3 1 ,given Zi ...29, . 28. As a function of x, find the precise distribution on the number of solutions a t o the equation x = { aC aC+1 where a and x are bytes with x given, and C give the average number of solutions.

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The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, nd the probability (a) That failure involves a gas leak (b) That there is evidence of electrical failure given that there was a gas leak (c) That there is evidence of a gas leak given that there is evidence of electrical failure 2-68. If P1A B2 1, must A B Draw a Venn diagram to explain your answer. 2-69. Suppose A and B are mutually exclusive events. Construct a Venn diagram that contains the three events A, B, and C such that P1A C2 1 and P1B C2 0

2-5 2-5.1

The de nition of conditional probability in Equation 2-5 can be rewritten to provide a general expression for the probability of the intersection of two events. This formula is referred to as a multiplication rule for probabilities.

29. For the PKZIP attack, experimentally determine the expected number of surviving Z-lists when n additional keystream bytes are used in the duplicate-reduction step, for n = 0 , 1 , 2 , . . . , m, where m is at least 10,000. For each n,run a t least 100 trials. Plot your results on a graph. 30. In Section 3.5.3 it is suggested that the weakest component in the PKZIP cipher is the use of the cyclic redundancy check (CRC), and we argue that a cryptographic hash function would be ideal. Suggest a possible replacement F for the CRC in PKZIP, where Y = F ( X ,b ) , where X and Y are 32-bits, and b is a byte. Your function F must be computationally efficient and only require a small number of lines of code. Explain why your suggested replacement is better than the CRC used in PKZIP.

Multiplication Rule P1A B2 P1B A2P1A2 P1A B2P1B2 (2-6)

Aperture Priority AE mode, denoted as Av on the Mode dial, is the semiautomatic mode of preference for everyday shooting because it offers quick control over the aperture, and, thus, control over one factor that determines depth of eld. In this mode, you control the aperture by turning the Control dial, and the camera automatically calculates the appropriate shutter speed based on the light meter reading, the metering mode, and the ISO Speed setting. The PowerShot G11 displays the selected aperture on the LCD monitor in white.

The last expression in Equation 2-6 is obtained by interchanging A and B. EXAMPLE 2-20 The probability that an automobile battery subject to high engine compartment temperature suffers low charging current is 0.7. The probability that a battery is subject to high engine compartment temperature is 0.05. Let C denote the event that a battery suffers low charging current, and let T denote the event that a battery is subject to high engine compartment temperature. The probability that a battery is subject to low charging current and high engine compartment temperature is P1C T 2 P1C T 2P1T 2 0.7 0.05 0.035

4

2-5.2

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