CHAPTER 5 Discrete Probability DistributionsIdentifying Probability Distributions. In Exercises 7-14, determine whether a prob-ability distribution is given. If a probability distribution is given, find its mean and standarddeviation. If a probability distribution is not given, identify the requirements that are notsatisfied.P(x)7. Genetic Disorder Five males with an X-linked genetic disorderhave one child each. The random variable x is the number of chil-dren among the five who inherit the X-linked genetic disorder.X0.03100.15610.31320.31330.15640.03158. Male Color Blindness When conducting research on colorblindness in males, a researcher forms random groups with fivemales in each group. The random variable x is the number of malesin the group who have a form of color blindness (based on data fromthe National Institutes of Health)P(x)X0.65900.28710.05020.00430.0010+59. Pickup Line Ted is not particularly creative. He uses the pickupline "If I could rearrange the alphabet, I'd put U and I together."The random variable x is the number of women Ted approachesbefore encountering one who reacts positivelyP(x)X0.00110.00920.0300.060410. Fun Ways to Flirt In a Microsoft Instant Messaging survey,respondents were asked to choose the most fun way to flirt, and theaccompanying table is based on the results.P(x)E-mail0.06In person0.55Instant0.24messageТеxt0.15message11. Fun Ways to Flirt A sociologist randomly selects single adultsP(x)of three, and the random variable x is the num-that the most fun way to flirt is infor differentgroupswho00.091saypersonber in thegroup10.334(based on a Microsoft Instant Messaging survey).20.40830.16612. Self-Driving Vehicle Groups of adults are randomly selectedand arranged inP(x)of three. The random variable x is the num-groupswho00.358that they would feel comfortable in a self-sayber in thegroup10.439driving vehicle (based on a TE Connectivity survey).20.17930.024LOLO

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CHAPTER 5 Discrete Probability Distributions
Identifying Probability Distributions. In Exercises 7-14, determine whether a prob-
ability distribution is given. If a probability distribution is given, find its mean and standard
deviation. If a probability distribution is not given, identify the requirements that are not
satisfied.
P(x)
7. Genetic Disorder Five males with an X-linked genetic disorder
have one child each. The random variable x is the number of chil-
dren among the five who inherit the X-linked genetic disorder.
X
0.031
0
0.156
1
0.313
2
0.313
3
0.156
4
0.031
5
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
the National Institutes of Health)
P(x)
X
0.659
0
0.287
1
0.050
2
0.004
3
0.001
0+
5
9. Pickup Line Ted is not particularly creative. He uses the pickup
line "If I could rearrange the alphabet, I'd put U and I together."
The random variable x is the number of women Ted approaches
before encountering one who reacts positively
P(x)
X
0.001
1
0.009
2
0.030
0.060
4
10. Fun Ways to Flirt In a Microsoft Instant Messaging survey,
respondents were asked to choose the most fun way to flirt, and the
accompanying table is based on the results.
P(x)
E-mail
0.06
In person
0.55
Instant
0.24
message
Теxt
0.15
message
11. Fun Ways to Flirt A sociologist randomly selects single adults
P(x)
of three, and the random variable x is the num-
that the most fun way to flirt is in
for different
groups
who
0
0.091
say
person
ber in the
group
1
0.334
(based on a Microsoft Instant Messaging survey).
2
0.408
3
0.166
12. Self-Driving Vehicle Groups of adults are randomly selected
and arranged in
P(x)
of three. The random variable x is the num-
groups
who
0
0.358
that they would feel comfortable in a self-
say
ber in the
group
1
0.439
driving vehicle (based on a TE Connectivity survey).
2
0.179
3
0.024
LO
LO
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CHAPTER 5 Discrete Probability Distributions Identifying Probability Distributions. In Exercises 7-14, determine whether a prob- ability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. P(x) 7. Genetic Disorder Five males with an X-linked genetic disorder have one child each. The random variable x is the number of chil- dren among the five who inherit the X-linked genetic disorder. X 0.031 0 0.156 1 0.313 2 0.313 3 0.156 4 0.031 5 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 the National Institutes of Health) P(x) X 0.659 0 0.287 1 0.050 2 0.004 3 0.001 0+ 5 9. Pickup Line Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of women Ted approaches before encountering one who reacts positively P(x) X 0.001 1 0.009 2 0.030 0.060 4 10. Fun Ways to Flirt In a Microsoft Instant Messaging survey, respondents were asked to choose the most fun way to flirt, and the accompanying table is based on the results. P(x) E-mail 0.06 In person 0.55 Instant 0.24 message Теxt 0.15 message 11. Fun Ways to Flirt A sociologist randomly selects single adults P(x) of three, and the random variable x is the num- that the most fun way to flirt is in for different groups who 0 0.091 say person ber in the group 1 0.334 (based on a Microsoft Instant Messaging survey). 2 0.408 3 0.166 12. Self-Driving Vehicle Groups of adults are randomly selected and arranged in P(x) of three. The random variable x is the num- groups who 0 0.358 that they would feel comfortable in a self- say ber in the group 1 0.439 driving vehicle (based on a TE Connectivity survey). 2 0.179 3 0.024 LO LO

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Expert Answer

Step 1

Consider, X be the random variable that represents the number if adults who feel comfortable in a self-driving vehicle.

0
1
2
P(X)
0.179
0.024
0.358
0.439
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0 1 2 P(X) 0.179 0.024 0.358 0.439

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Step 2

A probability distribution function must satisfy the following conditions:

  1. Sum of probabilities must be equal to 1.
  2. Probabilities must lie between 0 and 1.

Here, conditions required for a probability distribution are satisfied because probabilities are between 0 and 1 and sum of probabilities is equal to 1 which can be shown as:

Sum of probabilities =0.358+0.439+0. 179+0.024
=1
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Sum of probabilities =0.358+0.439+0. 179+0.024 =1

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Step 3

Since, both the conditions for a probability distribution function are sati...

E(X) - ΣΧ P(X
=0(0.358)+1(0.439) + 2 (0.179)+ 3 (0.024)
= 0.869
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E(X) - ΣΧ P(X =0(0.358)+1(0.439) + 2 (0.179)+ 3 (0.024) = 0.869

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