Query - Continuous Random Variable
- Thread starter Avishek
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I can't make sense of it. The 2 properties of a probability function are p(x) lies between 0 and 1, inclusive, and the sum of all p(x) must equal one (mutually exclusive, cumulatively exhaustive). If a p(x) is always zero for all X, then sum of p(x) can't be one, it omits outcomes, and isn't a probability function - David
David
This was the question. Can you build upon your explanation further. I have understood what exactly you tried to explain in the reading. But I failed to solve the below. Am I missing something?
Question: For a continuous random variable X, the probability of any single value of X is:
A) one.
B) zero.
C) determined by the cumulative function.
D) determined by the probability density function (pdf).
Your answer: B was correct!
For a continuous distribution p(x) = 0 for all X; only ranges of value of X have positive probabilities.
Thanks, Avi
This was the question. Can you build upon your explanation further. I have understood what exactly you tried to explain in the reading. But I failed to solve the below. Am I missing something?
Question: For a continuous random variable X, the probability of any single value of X is:
A) one.
B) zero.
C) determined by the cumulative function.
D) determined by the probability density function (pdf).
Your answer: B was correct!
For a continuous distribution p(x) = 0 for all X; only ranges of value of X have positive probabilities.
Thanks, Avi
Avi,
If that is my question, i need to fix it. Strictly speaking, the answer is correct but you are unlikely to encounter phrased this way due to its imprecision.
Under a discrete distribution, P(x) has some value.
Under a continuous distribution, there are no discrete outcomes. For example, time and distance are continuous variables; strictly speaking, you don't say P(3 feet away, or 3 seconds) because these values don't exist on a continuum. You would say P(2.99 feet < X < 3.01, or 2.9 seconds < X < 3.01 seconds).
That's what the explanation means, that P(X) = ? is NOT MEANINGFUL for a continuos distribution. We must say P(x1 <= X <= x2). That's the "only ranges" part...
David
If that is my question, i need to fix it. Strictly speaking, the answer is correct but you are unlikely to encounter phrased this way due to its imprecision.
Under a discrete distribution, P(x) has some value.
Under a continuous distribution, there are no discrete outcomes. For example, time and distance are continuous variables; strictly speaking, you don't say P(3 feet away, or 3 seconds) because these values don't exist on a continuum. You would say P(2.99 feet < X < 3.01, or 2.9 seconds < X < 3.01 seconds).
That's what the explanation means, that P(X) = ? is NOT MEANINGFUL for a continuos distribution. We must say P(x1 <= X <= x2). That's the "only ranges" part...
David
Yes David.
You are absolutely right. The phrase was pretty confusing. I think the below is a better question from this LOS ->
Question: For a continuous random variable X, the probability of any single value of X is:
A) one.
B) zero.
C) determined by the cumulative function.
D) determined by the probability density function (pdf).
Your answer: B was correct!
For a continuous distribution p(x) = 0 for all X; only ranges of value of X have positive probabilities.
Thanks, Avi
You are absolutely right. The phrase was pretty confusing. I think the below is a better question from this LOS ->
Question: For a continuous random variable X, the probability of any single value of X is:
A) one.
B) zero.
C) determined by the cumulative function.
D) determined by the probability density function (pdf).
Your answer: B was correct!
For a continuous distribution p(x) = 0 for all X; only ranges of value of X have positive probabilities.
Thanks, Avi
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