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Determine the following: (a) P 1X 2, Z 3 Y 172 (b) P 1X 2 Y 172 (c) E 1X 0 Y 172 5-23 An order of 15 printers contains four with a graphicsenhancement feature, ve with extra memory, and six with both features Four printers are selected at random, without replacement, from this set Let the random variables X, Y, and Z denote the number of printers in the sample with graphics enhancement only, extra memory only, and both, respectively (a) Describe the range of the joint probability distribution of X, Y, and Z (b) Is the probability distribution of X, Y, and Z multinomial Why or why not 5-24 Continuation of Exercise 5-23 Determine the conditional probability distribution of X given that Y 2 5-25 Continuation of Exercise 5-23.

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Determine the following: (a) P1X 1, Y 2, Z 12 (b) P1X 1, Y 12 (c) E1X 2 and V1X 2 5-26 Continuation of Exercise 5-23 Determine the following: (a) P1X 1, Y 2 Z 12 (b) P1X 2 Y 22 (c) The conditional probability distribution of X given that Y 0 and Z 3 5-27 Four electronic ovens that were dropped during shipment are inspected and classi ed as containing either a major, a minor, or no defect In the past, 60% of dropped ovens had a major defect, 30% had a minor defect, and 10% had no defect Assume that the defects on the four ovens occur independently.

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The parsing function is only somewhat lenient; it is better suited for interpreting speci cally computer-formatted dates than free-form human input. It s always a good idea to check a date s validity after constructing it from a string. You can check a date s validity by checking whether its epoch time is a number.

(a) Is the probability distribution of the count of ovens in each category multinomial Why or why not (b) What is the probability that, of the four dropped ovens, two have a major defect and two have a minor defect (c) What is the probability that no oven has a defect.

var invalid:Date = new Date("Yesterday"); trace(invalid); // Invalid Date trace(isNaN(invalid.valueOf())); // true

5-28 Continuation of Exercise 5-27 Determine the following: (a) The joint probability mass function of the number of ovens with a major defect and the number with a minor defect (b) The expected number of ovens with a major defect (c) The expected number of ovens with a minor defect 5-29 Continuation of Exercise 5-27 Determine the following: (a) The conditional probability that two ovens have major defects given that two ovens have minor defects (b) The conditional probability that three ovens have major defects given that two ovens have minor defects (c) The conditional probability distribution of the number of ovens with major defects given that two ovens have minor defects (d) The conditional mean of the number of ovens with major defects given that two ovens have minor defects 5-30.

So what is this so-called epoch time I don t know. Hmm . . . maybe somewhere in this big book there is a section called . . .

In the transmission of digital information, the probability that a bit has high, moderate, or low distortion is 001, 004, and 095, respectively Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent (a) What is the probability that two bits have high distortion and one has moderate distortion (b) What is the probability that all three bits have low distortion 5-31 Continuation of Exercise 5-30 Let X and Y denote the number of bits with high and moderate distortion out of the three transmitted, respectively Determine the following: (a) The probability distribution, mean and variance of X (b) The conditional probability distribution, conditional mean and conditional variance of X given that Y 2 5-32.

In simpler times, people didn t have Date classes or fancy laptops or terabyte hard drives full of 30 Rock episodes in HD. Folks then, they had a big ol heap of memory and some simple types that stored some simple values. When they needed a time value and people always needed a time value they relied on their old friend int. Remember that old tale about time just being a number Well, it sure can be, if you can just decide what time was 0. So those folks did just that. They stored a time as a number of seconds since another time, and they put that number right in an int. What was the time those folks measured against It was the Epoch: midnight, January 1, 1970. But why that day The epoch of what This is the way time has always been represented in Unix, and

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