Question

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 (based on a Microsoft Instant Messaging survey).

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.

Answer 1

This data is not a probability distribution

The reason sum of the probabilities is not equal

∑ P(X=x) ≠ 1

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

`p_(i) = P(x=x_(i)) = p(x_(i)) for I= 1,2,3......`

If the numbers
`p(x_(i)) , I =1 ,2,3,.....` satisfy the two conditions

i)
`p(x_(i)) \geq 0 for all values of i`

ii) ∑P(X=x) =1

Given data condition(i) satisfied
`p(x_(i)) \geq 0 for all values of i`

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