d. Numbers of randomly generated digits before getting the dig party affiliation

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d. Numbers of randomly generated digits before getting the dig party affiliations of adults in the United States f. Exact costs of presidential campaigns entifying Probability Distributions. n Exercises 7-14, determine whether a tst distribution is given. Ifa probability distribution is given, find its mean standard deviation. Ifa probability distribution is not given, identify the require- ments that are not satisfied probabili 7. Genetic Disorder Four males with an X-linked genetic d have one child cach. The random variable x is the number of chil dren among the four who inherit the X-linked genetic disorder P (x) 0.0625 0.2500 0.3750 0.2500 0 0625 3 8. Male Color Blindness When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness (based on data from 2 P (x) 0.659 0.287 0.050 0.004 0.001 the National Institutes of Health). P(x) 9. Pickup Line Ted is not particularly creative. He uses this pickup x line: "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of girls Ted approaches before encountering one who reacts positively 0.001 0.020 0.105 0.233 0.242 2 10. Fun Ways to Flirt In a Microsoft Instant Messaging survcy respondents were asked to choose the most fun way to flirt, and the accompanying table is based on the results. P(x) E-mail In person 0.55 Instant message 0.06 0.24 0.15 message 11. Fun Ways to Flirt A sociologist randomly selects single adults for different groups of four, and the random variable x is the num- ber in the group who say that the most fun way to flirt is in person (based on a Microsoft Instant Messaging survey). -x P (x) 0.041 0.200 0.367 0.299 0.092 0

Explanation / Answer

question 7

Here to be a probability distribution sum of all probabilities must be 1

so here ? p(x) = 1

0.0625 + 0.250 + 0.375 + 0.25 + 0.0625 = 1

Here mean E(x) = 0.0625 * 0 +  0.250 * 1 + 0.375 *2 + 0.25 *3 + 0.0625 * 4 = 2

Variance = Var(X) =   0.0625 * (0 -2)2 +  0.250 * (1 -2)2 + 0.375 *  (2 -2)2 + 0.25 *  (3 -2)2 + 0.0625 * (4 -2)2 = 1

STD(x) = sqrt (1) = 1

Question 8

Here to be a probability distribution sum of all probabilities must be 1

so here ? p(x) = 1

0.659 + 0.287 + 0.050 + 0.004 + 0.001 = 1.001 > 1 so not a probability distribution.

Question 9

Here to be a probability distribution sum of all probabilities must be 1

so here ? p(x) = 1

0.001 + 0.020 + 0.105 + 0.233 + 0.242 = 0.601 < 1 so not a probability distribution.

Question 10

Here to be a probability distribution sum of all probabilities must be 1

so here ? p(x) = 1

0.06 + 0.55 + 0.24 + 0.15 = 1 so it is a valid probability distribution

BUt the independent variable is a nominal variable not a ratio/interval variable so not a valid probability distribution.

Question 11

Here to be a probability distribution sum of all probabilities must be 1

so here ? p(x) = 1

0.041 + 0.200 + 0.367 + 0.299 + 0.092 = 0.999 < 1 but we can take it is as rounding error so we will count it is as a discrete probability distribution

Mean E(x) = 0 * 0.041 + 1 * 0.2 + 2 * 0.367 + 3 * 0.299 + 4 * 0.092 = 2.2

Var(x) = (0 -2.2)2 * 0.041 + (1 -2.2)2 * 0.2 + (2 -2.2)2 * 0.367 + (3 -2.2)2* 0.299 + (4 -2.2)2 * 0.092 = 0.99

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