the following probability density function. a. Select the probability density function. 1. 2. 3. 4. b. What is the probability of generating a random number between 0.15 and 0.85 (to 1 decimal place)? c. What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimal place)? d. What is the probability of generating a random number with a value greater than 0.6 (to 1 decimal place)? e. Using 50 random numbers given below, compute the mean and standard deviation. 0.467202 0.370629 0.966103 0.003795 0.877402 0.626396 0.816661 0.955063 0.569638 0.793645 0.641853 0.189704 0.519289 0.876775 0.016900 0.232961 0.807478 0.051656 0.469154 0.836005 0.381807 0.646180 0.038759 0.227787 0.801533 0.825934 0.600144 0.732024 0.332249 0.858704 0.807478 0.018977 0.564639 0.751811 0.100518 0.561720 0.331878 0.998821 0.071962 0.711114 0.070831 0.151657 0.637766 0.164211 0.933752 0.940995 0.873402 0.506010 0.893695 0.711803 Mean (to 6 decimals) Standard deviation (to 6 decimals)
the following probability density function. a. Select the probability density function. 1. 2. 3. 4. b. What is the probability of generating a random number between 0.15 and 0.85 (to 1 decimal place)? c. What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimal place)? d. What is the probability of generating a random number with a value greater than 0.6 (to 1 decimal place)? e. Using 50 random numbers given below, compute the mean and standard deviation. 0.467202 0.370629 0.966103 0.003795 0.877402 0.626396 0.816661 0.955063 0.569638 0.793645 0.641853 0.189704 0.519289 0.876775 0.016900 0.232961 0.807478 0.051656 0.469154 0.836005 0.381807 0.646180 0.038759 0.227787 0.801533 0.825934 0.600144 0.732024 0.332249 0.858704 0.807478 0.018977 0.564639 0.751811 0.100518 0.561720 0.331878 0.998821 0.071962 0.711114 0.070831 0.151657 0.637766 0.164211 0.933752 0.940995 0.873402 0.506010 0.893695 0.711803 Mean (to 6 decimals) Standard deviation (to 6 decimals)
the following probability density function. a. Select the probability density function. 1. 2. 3. 4. b. What is the probability of generating a random number between 0.15 and 0.85 (to 1 decimal place)? c. What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimal place)? d. What is the probability of generating a random number with a value greater than 0.6 (to 1 decimal place)? e. Using 50 random numbers given below, compute the mean and standard deviation. 0.467202 0.370629 0.966103 0.003795 0.877402 0.626396 0.816661 0.955063 0.569638 0.793645 0.641853 0.189704 0.519289 0.876775 0.016900 0.232961 0.807478 0.051656 0.469154 0.836005 0.381807 0.646180 0.038759 0.227787 0.801533 0.825934 0.600144 0.732024 0.332249 0.858704 0.807478 0.018977 0.564639 0.751811 0.100518 0.561720 0.331878 0.998821 0.071962 0.711114 0.070831 0.151657 0.637766 0.164211 0.933752 0.940995 0.873402 0.506010 0.893695 0.711803 Mean (to 6 decimals) Standard deviation (to 6 decimals)
Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.
a. Select the probability density function.
1.
2.
3.
4.
b. What is the probability of generating a random number between 0.15 and 0.85 (to 1 decimal place)?
c. What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimal place)?
d. What is the probability of generating a random number with a value greater than 0.6 (to 1 decimal place)?
e. Using 50 random numbers given below, compute the mean and standard deviation.
0.467202
0.370629
0.966103
0.003795
0.877402
0.626396
0.816661
0.955063
0.569638
0.793645
0.641853
0.189704
0.519289
0.876775
0.016900
0.232961
0.807478
0.051656
0.469154
0.836005
0.381807
0.646180
0.038759
0.227787
0.801533
0.825934
0.600144
0.732024
0.332249
0.858704
0.807478
0.018977
0.564639
0.751811
0.100518
0.561720
0.331878
0.998821
0.071962
0.711114
0.070831
0.151657
0.637766
0.164211
0.933752
0.940995
0.873402
0.506010
0.893695
0.711803
Mean (to 6 decimals)
Standard deviation (to 6 decimals)
Transcribed Image Text:Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let denote a random number generated using RAND, then is a continuous random variable with the following probability density function.
[1 for 0 ≤
≤1
f(x) = { 10 elsewhere
a. Select the probability density function.
1.
2.
3.
4,
f(x)
1.5-
1
0.5
f(x)
1.54
1
0.5
f(x)
1.5-
14
0.5-
f(x)
1.5-
1-
0.5
1
1
1
2
2
3
3
3
X
X
- Select your answer - V
b. What is the probability of generating a random number between 0.15 and 0.85 (to 1 decimal place)?
c. What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimal place)?
d. What is the probability of generating a random number with a value greater than 0.7 (to 1 decimal place)?
Transcribed Image Text:e. Using 50 random numbers given below, compute the mean and standard deviation.
Mean=
Standard deviation =
(to 6 decimals)
(to 6 decimals)
0.467202
0.626396
0.641853
0.232961
0.381807
0.825934
0.807478
0.561720
0.070831
0.940995
0.370629
0.816661
0.189704
0.807478
0.646180
0.600144
0.018977
0.331878
0.151657
0.873402
0.966103
0.955063
0.519289
0.051656
0.038759
0.732024
0.564639
0.998821
0.637766
0.506010
0.003795
0.569638
0.876775
0.469154
0.227787
0.332249
0.751811
0.071962
0.164211
0.893695
0.877402
0.793645
0.016900
0.836005
0.801533
0.858704
0.100518
0.711114
0.933752
0.711803
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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