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In Example 5-13, the marginal probability distribution of X2 is binomial with n 20 and p 0.3. Furthermore, the joint marginal probability distribution of X2 and X3 is found as follows. The P(X2 x2, X3 x3) is the probability that exactly x2 trials result in G and that x3 result in F. The remaining n x2 x3 trials must result in either E or P. Consequently, we can consider each trial in the experiment to result in one of three classes, {G}, {F}, or {E, P}, with probabilities 0.3, 0.08, and 0.6 0.02 0.62, respectively. With these new classes, we can consider the trials to comprise a new multinomial experiment. Therefore, fX2 X3 1x2, x3 2 P1X2 x2, X3 n! x2!x3! 1n x2 x3 2 x3 2!

Hours are measured in 24-hour/military time, so they can range from 0 (12 a.m.) to 23 (11 p.m.). You might notice that there s something shy with the dates as entered in the preceding code. Certain units in the Date class are zero-indexed, and certain units are one-indexed. Although January is the rst month, the Date class calls it zero. Properties are zero-indexed when they refer to named units, such as months (January, February, and so on) or days of the week (Monday, Tuesday, and so on). This way, you can use an array of month names to generate human-readable dates, as shown in Example 7-2.

The joint probability distribution of other sets of variables can be found similarly. EXERCISES FOR SECTION 5-2

var daysOfWeek:Array = ["domingo", "lunes", "martes", "mi rcoles", e "jueves", "viernes", "s bado"] a trace(daysOfWeek[timeOfWriting.day]); //lunes

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5-17. Suppose the random variables X, Y, and Z have the following joint probability distribution x 1 1 1 1 2 2 2 2 y 1 1 2 2 1 1 2 2 z 1 2 1 2 1 2 1 2 f (x, y, z) 0.05 0.10 0.15 0.20 0.20 0.15 0.10 0.05 Determine the following: (a) P 1X 22 (b) P 1X 1, Y 22 (c) P 1Z 1.52 (d) P 1X 1 or Z 22 (e) E 1X 2 5-18. Continuation of Exercise 5-17. Determine the following: (a) P 1X 1 Y 12 ( b ) P 1X 1, Y 1 Z 22 (c) P 1X 1 Y 1, Z 22 5-19. Continuation of Exercise 5-17. Determine the conditional probability distribution of X given that Y 1 and Z 2. 5-20. Based on the number of voids, a ferrite slab is classi ed as either high, medium, or low. Historically, 5% of the slabs are classi ed as high, 85% as medium, and 10% as low.

By representing these named parts of time as numbers, they remain language independent. Months and days of the week are indexed from zero. Days of the month are indexed from one. Hours, minutes, seconds, and milliseconds are measured from zero. Years are measured from zero (AD 0/CE 0). A third way to create a Date object is by passing it a string representing a time. The string must contain at minimum a year, month, and day of the month, but it can contain more. If the Date constructor can t gure out how to get a date out of your string, it creates a new Date with an Invalid Date value, the equivalent of a NaN. All of the following lines create valid dates:

A sample of 20 slabs is selected for testing Let X, Y, and Z denote the number of slabs that are independently classi ed as high, medium, and low, respectively (a) What is the name and the values of the parameters of the joint probability distribution of X, Y, and Z (b) What is the range of the joint probability distribution of X, Y, Z (c) What is the name and the values of the parameters of the marginal probability distribution of X (d) Determine E1X 2 and V 1X 2 5-21 Continuation of Exercise 5-20 Determine the following: (a) P 1X 1, Y 17, Z 32 (b) P 1X 1, Y 17, Z 32 (c) P 1X 12 (d) E 1X2 5-22 Continuation of Exercise 5-20.

new new new new Date("1/28/2007"); // United States style MM/DD/YYYY Date("Sun Jan 28 2007"); Date("28 Jan 2007"); Date("Sun Jan 28 2007 3:16:12 PM");

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