Question

1.Determine whether the following value is a continuous random​ variable, discrete random​ variable, or not a random variable.

a. The number of runs scored during a baseball game number of runs scored during a baseball game

b. The last book a person in City Upper A read last book a person in City A read

c. The number of people in a restaurant that has a capacity of 200number of people in a restaurant that has a capacity of 200

d. The time it takes for a light bulb to burn out time it takes for a light bulb to burn out

e. The time it takes to drive from City Upper A to City Upper B time it takes to drive from City A to City B

f. The number of pigeons in a country number of pigeons in a country

2.

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. Determine whether a probability 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. Find the mean of the random variable x. Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the box. 3. Refer to the accompanying​ table, which describes the number of adults in groups of five who reported sleepwalking. Find the mean and standard deviation for the numbers of sleepwalkers in groups of five. The mean is _____ nothing sleepwalker(s). ​(Round to one decimal place as​ needed.) The standard deviation is _____ nothing sleepwalker(s). ​(Round to one decimal place as​ needed.) x ​P(x) 0 0.163 1 0.357 2 0.308 3 0.137 4 0.033 5 0.002		x	​P(x)
		0	0.001
		1	0.008
		2	0.035
		3	0.056

Answer 1

1)

a) It is a discrete random variable.

b) It is not a random variable.

c) It is a discrete random variable.

d) It is a Continuous random variable.

e) It is a Continuous random variable.

f) It is a discrete random variable.

2)

X	P(X)
0	0.001
1	0.008
2	0.035
3	0.056
Total	0.1

  

Total Probability = 1

Here, Probability condition is not satisfied.

3)

Table:

X	P(X)	X*P(X)	X2*P(X)
0	0.163	0	0
1	0.357	0.357	0.357
2	0.308	0.616	1.232
3	0.137	0.411	1.233
4	0.033	0.132	0.528
5	0.002	0.01	0.05
Total	1	1.526	3.4

Here,

Mean [E(X)] = 1.5

First We have to find out Variance.

V(X) = E(X²) - [E(x)]²

V(X) = 3.4 - (1.5²)

V(X) = 1.1

Now, We find out standard deviation (SD)

Therefore,

Mean = E(X) = 1.5

SD = 1.0