Practicing math exercises is an integral part of perfecting math skills. When yo

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Practicing math exercises is an integral part of perfecting math skills. When you practice, you identify mistakes that can happen and improve with each mistake. Taking a test in math without practicing the concepts can lead to unsatisfactory results Therefore, you must complete the homework in MyStatlab before you answer these questions. Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain Respond to AT LEAST TWO of your classmates' posts. It their work similar to your own' Do you understand their answers? Keep in mind this rubric when responding to your classmates: "Student responds with thorough and constructive analysis to at least two classmates, relating the response to relevant course concepts. Student may pose pertinent follow-up thoughts or questions about the topic, and demonstrates respect for the diverse opinions of fellow learners." Scoring will be based on: Critical Thinking Skits Participation Coherence & Organization

Explanation / Answer

Answer to the question:- If the expected value of the probability distribution of a random variable always one of the possible values of X? Explain.

As we know that there are two properties of any probability distribution:-

1. The probability of any specific outcome for a discrete random variable must be between 0 and 1. Stated mathematically, 0<=f(x=k)<=1, for all values of k.

2. The sum of the probabilities over all possible values of a discrete random variable must equal 1.

Now, say we have an unbiased dice and the possible outcomes can either be 1, 2, 3,4,5 or 6. We have a defined universe here and the probability of each outcome is 1/6 thereby meeting the first property and if we add up, it makes 1/6*6 = 1, meeting the 2nd property as well.

now, if we through the dice randomly, the expected value would be any of the six outcomes only. These six outcomes are probable event. Hence, we can say that the expected value would be any of the probable values only.

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