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Amber Quinn

Amber Quinn

Answered question

2022-06-17

Suppose
f X ( x ) = { 0.5 x = 0 x 0 < x 1
What is the MODE of this distribution? I think it should be 0 because it has the highest mass, even though 1 has the highest density.
Another one
f X ( x ) = { x 0 < x 1 1 1 < x 1.5
What would be the MODE in this case? 1 ?     1.5 ? or any number in [ 1 , 1.5 ]

Answer & Explanation

Cristopher Barrera

Cristopher Barrera

Beginner2022-06-18Added 24 answers

This is a bit controversial. If you go according to the definition of mode. It is the value of the random variable with the highest probability.
If you compare a point (with non-zero probability) from a discrete distribution to that of a continuous distribution, you will clearly notice that probability at a point for the discrete distribution would be non-zero.
Though, the probability of the continuous distribution at a point would be zero. (Because the probability is spread over infinite values inside the range, with some points having more density than the others.)
Following that logic, x = 0 would be the mode of your first question.
For the second part of your question, this is a matter of the mode not being clearly defined.
Ask yourself the question. What is the mode from the following discrete distribution? { 1 , 2 , 3 , 3 , 4 , 5 , 5 }
Is it 3 or 5? Similar is the ambiguity in the second question at hand.
pachaquis3s

pachaquis3s

Beginner2022-06-19Added 4 answers

An element x S that maximizes the probability density function f is called a mode of the distribution.
In the first case, it is x = 1 and in the second case, it is any number between [ [ 1 , 1.5 ] .

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