Finding the prob. in a continuous uniform distribution (z values)

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rogo0034
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Homework Statement



Printed problem 6.2: Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional probability P(X > 2.5 | X ≤ 4).


Homework Equations



Formula for a z-score: Z = (X − μ) / σ, where X is the value, μ the mean and σ the standard deviation.


The Attempt at a Solution



I understand that all i need to do is plug these two points into the formula and subtract to get the correct area, but i am not provided a mean or variance as i normally am, so I'm at a loss.
 
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What does that formula for Z have to do with the original question? Do you know what the definition of a uniform distribution is (i.e. can you write down the density function)
 
Here's what we are given in one of the examples helping to explain it to us.

Equation for the probability that X lies between x1 and x2 as the integral of the normal density n(x; mu, sigma) from x1 to x2, equal to 1 over the square root of 2 pi sigma times the integral of e raised to minus (x minus mu) squared over 2 sigma squared, dx.


I put in the formula for Z because if i had the standard deviation and mean, this would be extremely simple (for me)
 
Office_Shredders gentle question is a hint that the normal distribution has nothing to do with the problem. Try answering the questions he posed.
 
Office_Shredder said:
What does that formula for Z have to do with the original question? Do you know what the definition of a uniform distribution is (i.e. can you write down the density function)

In addition to this, since the distribution in question is uniform, I suggest to draw a picture :-) In this case it would be very self-explanatory.
 
OK, so this isn't helping yet, I'm still under the impression that in order to solve this problem, i need the mean (which I'm assuming is 3), and the standard deviation from the mean (which I'm at a loss for). Anyone able to help explain this better, it's the first question in my homework and i feel I'm just over thinking it?
 
rogo0034 said:
OK, so this isn't helping yet, I'm still under the impression that in order to solve this problem, i need the mean (which I'm assuming is 3), and the standard deviation from the mean (which I'm at a loss for). Anyone able to help explain this better, it's the first question in my homework and i feel I'm just over thinking it?

Why are you assuming the mean is 3? Don't you know how to calculate the mean?

1. What is the density function for this problem?
2. What is the formula for the mean? Does it give 3?
3. What is the formula for variance? What does it give?

Show us some work. And, as an aside, are you sure calculating the mean and variance is what you need for this problem? What is the formula for P(A|B)?
 
Last edited:
I'm assuming the mean is 3 because it is a uniform distribution 1 through 5, which would make the mean three... right? (two units on each side, central tendency). I don't have any more information about this problem than is given, but since it is a normal uniform distribution, it should fit into this distribution:

Handwritten derivation: P(1 < X < 5) = integral from 1 to 5 of n(x; μ, σ) dx = integral from 1 to 5 of (1/√(2πσ)) e^(-(1/(2σ²))(x-μ)²) dx


I don't have formulas for the mean or variance, alls i have a proofs that the expected value of (x) is the mean, and the expected value of (x minus the mean squared) is the SD.
 
Great, i finished the sections homework without any issues, took no time at all, except for this one problem, I must be over thinking it...?? this problem seems like it should be so simple.
 
LCKurtz said:
Why are you assuming the mean is 3? Don't you know how to calculate the mean?

1. What is the density function for this problem?
2. What is the formula for the mean? Does it give 3?
3. What is the formula for variance? What does it give?

Show us some work. And, as an aside, are you sure calculating the mean and variance is what you need for this problem? What is the formula for P(A|B)?

rogo0034 said:
I'm assuming the mean is 3 because it is a uniform distribution 1 through 5, which would make the mean three... right? (two units on each side, central tendency). I don't have any more information about this problem than is given, but since it is a normal uniform distribution, it should fit into this distribution:

Handwritten equation: P(1 < X < 5) = integral from 1 to 5 of n(x; μ, σ) dx = integral from 1 to 5 of (1/√(2πσ)) e^(-(x-μ)²/(2σ²)) dx.


I don't have formulas for the mean or variance, alls i have a proofs that the expected value of (x) is the mean, and the expected value of (x minus the mean squared) is the SD.

rogo0034 said:
Great, i finished the sections homework without any issues, took no time at all, except for this one problem, I must be over thinking it...?? this problem seems like it should be so simple.

Yes, it would be simple if you would just answer the questions I and others have asked. Why do you keep mentioning the normal distribution, even after you have acknowledged it is a uniform distribution?

Among other suggestions, I have highlighted in dark blue two questions you have ignored. Answering those two questions is necessary to proceed. And to answer what the density function is, I mean a formula.
 
Last edited:
ahhhh, for some reason i was thinking this was a bell curve the whole time. But, because of that realization, i found the formulas for mean and SD, and plugged them into the formula originally given. Sorry the quality is terrible, but here's what i got.

Handwritten work on paper: P(X > 2.5 | X ≤ 4) = P(2.5 < X ≤ 4), integral of 1/5 dx, mean = (0+5)/2 = 2.5, variance = (5-1)^2/12 = 1.3, z = (4-3)/σ = .8660 → .8078, z = (2.5-3)/σ = -.433 → .3336, then (.8078) - (.3336) = .4742, with 47.4270 written below.
 
You keep going back to thurs formula for normal distributions, but you don't have a normal distribution.

I think maybe a more basic question is in order: what's the definition of a density function?
 
And he still hasn't give the formula f(x) for the density or the formula for P(A|B). Rogo0034 if you can't answer those two questions you need more help than I can give you. I'm sure they are in your textbook.
 

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