# A sociologist randomly selects single adults for different groups of three, and the random variable

###### Question:

x P(x)

0 0.091

1 0.334

2 0.408

3 0.166

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.

## Answers

This data is not a probability distribution

The reason sum of the probabilities is not equal

∑ P(X=x) ≠ 1

Step-by-step explanation:

Explanation:-

Given data

x 0 1 2 3

p(x) 0.091 0.334 0.408 0.166

Discrete distribution :-

Probability distribution of a random variable is the set of its possible values together with their respective probabilities. Suppose X is a discrete random variable with possible outcomes (values) x₁ , x₂ , x₃ ,......... The probability of each possible outcome

[tex]p_{i} = P(x=x_{i}) = p(x_{i}) for I= 1,2,3......[/tex]

If the numbers [tex]p(x_{i}) , I =1 ,2,3,.....[/tex] satisfy the two conditions

i) [tex]p(x_{i}) \geq 0 for all values of i[/tex]

ii) ∑P(X=x) =1

Given data condition(i) satisfied [tex]p(x_{i}) \geq 0 for all values of i[/tex]

but the condition (ii) is not satisfied

0.091+0.334+ 0.408+ 0.166 = 0.999

sum off all probabilities is not equal to one

Conclusion:-

The given data is not probability distribution

A.

Yes, the table shows a probability distribution.

Step-by-step explanation:

Given that 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.

Since sample size is only 3, x cannot be more than 3.

So x can take values as 0 1 2 3

Prob distribution is given as

xP(x)

00.092

10.338

20.418

30.152

We find that x values are from 0 to 3.

Each probability is positive but less than 1.

Also total probability = 1

So this is a perfect probability distribution.

A.

Yes, the table shows a probability distribution.

A. Yes, the table shows a probability distribution.

Step-by-step explanation:

In a probability distribution, none of the values can be negative or over 1. Additionally, all of the values must sum to 1.

Our probabilities are:

0.087; 0.328; 0.416; and 0.169. None of these are negative and none are over 1.

0.087+0.328+0.416+0.169 = 1.00; this means that this is a probability distribution.

Srry i cant u there i just dont understand