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Function P is a function defined on the set of real numbers. We do not know...

Function P is a function defined on the set of real numbers. We do not know the value of P for all cases, but  it is known that P(x) = 0.3 when 0 <= x <= 10.  Is P definitely a probability density function, possibly a probability density function, or definitely not a probability density function? Explain your answer.

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Answer #1

We have been given the following information:

  • Function P is a function defined on the set of real numbers.
  • P(x) = 0.3 when 0 <= x <= 10

Based on this given information we can say that "P is possibly a probability density function"

For P to be a pdf the over its entire range (in this case the set of real numbers) should be 1.

We know for sure that for a defined interval 0 <= x <= 10, P(x) = 0.3

If P(x) = 0.7 for the rest of its range, then we have P as a pdf otherwise not. So there is a chance of P being a probability density function.
If satisfied, please do upvote! Let me know in the comments if anything is unclear. I will reply ASAP

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