Provide an example of a discrete probability distribution by making up a hypothe

Question

Provide an example of a discrete probability distribution by making up a hypothetical example with five data points (scores) and arbitrarily assign associated frequencies to each of those scores, then respond to the prompts below.

List the five data points (scores) and their frequencies here.

Calculate the probability of each score and list them here.

Do the probabilities listed in the answer to the previous question make up a probability distribution?

How do you know?

Calculate the mean of the probability distribution described in the answers to the previous questions.

Calculate the standard deviation of the probability distribution described in the answers to the previous questions.

Explanation / Answer

Consider the following example,

x : scores

f : frequency of scores

P(x) : probability corresponding to that scores.

Probability distribution of x is,

It is a probability distribution because sum of all probabilities corresponding to x is equal to 1

Mean = sum(x * P(x = x))

= 1 * 0.16 + 2*0.22 + 3 * 0.28 +4 * 0.20 + 5 * 0.14

= 2.94

Mean = 2.94

Standard deviation = sum(sqrt(( x - Mean)2 * P(x)))

Standard deviation = sqrt( 1.616) = 1.271

Standard deviation = 1.271

This is a one type way of answering question here I donot know the previous way of answering the question.   

x f P(x) 1 24 24 / 150 = 0.16 2 33 33 / 150 = 0.22 3 42 42 / 150 =0.28 4 30 30 / 150 = 0.20 5 21 21 / 150 = 0.14 Total 150 1

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