A sociologist randomly selects single adults for different groups of​ three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. 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. x ​P(x) 0 0.087 1 0.344 2 0.415 3 0.154

Answers

Answer 1

Answer:

Yes the table shows a probability distribution

The mean is [tex]E(X) = 1.636 [/tex]

The  standard deviation is   [tex]\sigma = 0.845 [/tex]

Step-by-step explanation:

From the question we are told that

The data given is

x 0 1 2 3

P(x) 0.087 0.344 0.415 0.154

Generally we can evaluate [tex]P(x) * x[/tex] as

[tex]P(x) * x[/tex] 0 (1 * 0.344 ) (2 * 0.415) (3 * 0.154 )

=> [tex]P(x) * x[/tex] 0 0.344 0.830 0.462

Generally we can evaluate [tex]P(x) * x^2 [/tex] as

[tex]P(x) * x^2 [/tex] 0 [tex ](1^2 * 0.344 )[/tex] [tex ](2^2 * 0.415)[/tex] [tex ](3^2 * 0.154 )[/tex]

=> [tex]P(x) * x^2 [/tex] 0 [tex] 0.344 [/tex] [tex ]1.66 [/tex] [tex]1.386[/tex]

Generally the mean is mathematically represented as

[tex]E(X) = \sum [x* P(x)][/tex]

[tex]E(X) = 0 + 0.344+ 0.830+0.462 [/tex]

[tex]E(X) = 1.636 [/tex]

Generally the standard deviation is mathematically represented as

[tex]\sigma = \sqrt{V(X)}[/tex]

Here [tex]V(X)[/tex] is the variance which is mathematically represented as

[tex]V(X) = [E(X^2) ]- [E(X)]^2[/tex]

Here

[tex]E(X^2) = \sum [x^2 * P(x)][/tex]

[tex]E(X) =0 +0.344+1.66+1.386 [/tex]

[tex]E(X) = 3.3900 [/tex]

So

[tex]V(X) = 3.3900 - [1.636]^2[/tex]

[tex]V(X) = 3.3900 - 2.6764[/tex]

[tex]V(X) = 0.7136[/tex]

So

[tex]\sigma = \sqrt{0.7136}[/tex]

[tex]\sigma = 0.845 [/tex]


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