Question

I am willing to work! I want to learn!
Topic: Probability Distributions (Algebra II)
I will post additional information once thread becomes active. Thanks.

Answer 1

Which statements explain that the table does not represent a probability distribution?

TABLE Result / Probability

Result: -2 Probability: 2/3
Result: -4 Probability: 1/12
Result: -6 Probability: 5/3
Result: -8 Probability: 1/6

Possible Answers: (Select all the Apply)

1. The probabilities have different denominators.

It is true, but I find no reason on why that would be considered a problem.

2. The results are all less than 0.

Each probability is a number between 0 and 1. Fact. That being I would select, “The results are less than 0”. Our results are negative. (Selection)

3. The sum of the probabilities is 31/12.

True. That is what the probabilities total, but do you think this is a trick question in which they’re looking for a more explicit answer? For example, the sum of the probabilities is 31/12, which is greater than 1 and thus incorrect. Despite this I also hesitantly select this as one my answers. (Selection)

4. The probability 5/3 is greater than 1.

This is true, but is it true enough. It states that the sum of all probabilities is equal to 1, but 5/3 certainly isn’t all probabilities its just one of them. (Selection?)

I’m just looking for some second opinions and verification of my own.

Answer 2

@mathmate I hate to bother 'tutors' like yourself, especially begging, but I'm generally curious about the answer. I can't tell if I'm overthinking it or not understanding it. Thanks.

Answer 3

The sum of the probabilities is 31/12.
The probability 5/3 is greater than 1.

Answer 4

Ah! It says each, "Each probability is a number between 0 and 1", but is dose NOT say that about the results. My bad, I should have the read question better. Thanks for your help.

Answer 5

Any probability distributions should:

1. include the value of (non-zero) probability for all possible outcomes, between [-inf, inf].
The usual convention is that unmentioned outcomes has a probability of zero, i.e. never happens.

2. The sum of the probabilities of all possible outcomes equals exactly 1.0, which means that it is certain to fall into one of the mentioned possible outcomes (and nothing else).

Mathematically, #2 above means that if it is a discrete distribution, then
\(\sum\) pi =1, i=all possible outcomes.
If the distribution is continuous, then
\(\int_{-\infty}^{+\infty} p(x)dx\)=1.0