I'm an actual civil engineer and I don't know how to solve that (I've been out of school for 10 years though). In actual practice, I don't think statistical analysis is used in structural problems, maybe in water resources problems.

 

yeah, this stuff is major overkill, not only that the exam is tomorrow.

 

 

Well with a cursory glance perhaps I can help if its not too late but is there some missing information?

It sounds like your X is composed of some discrete values.

The expected value I can compute now (based on wikipedia for 'expected value'):
its just the integral of the x*f(x) = -ln(x) + x - 1/x

The last two parts of the question are easy, since you have the PDF you know the probability of any x occuring. Take and solve for 3. Then solve for the boundary conditions 1 to 3 with the CDF.

The integral is:

solving for x=3 yields a probability of 26% or so.
using ln(x) + 1/x - 1/(2x^2), and ntegrating from 1->3 yields a prob of 88% or so.

I'm not sure on the mode or median (I feel like this is where information might be missing) but the mean is the point at which the CDF = .5 (when x=1 according to my calculations). I don't know if that helps with the problem, but an fyi.

 

I think its already normalized. The trick is that the CDF has an x-intercept from negative to positive at .678. From here I think you can compute the integratable values. Or maybe thats not what you meant. Either way, the above posted function is not a normal distribution.

 

....42

 

Thank you that helps a lot. Are you an engineer? student? Do you use this a lot in your practice?

 

I did my grad and undergrad in computer engineering, im currently in a phd for biomedical engineering.

We definitely use statistics, and for your problem I'd say they can be universally applied. Although I don't know how often you'd use that problem in that particular context, I'll bet you'll use the mathematics much more often.

 

This is the other problem I need to solve, any insight on how to do it? Thanks for the help!



Monthly rainfalls in a tropical city are independents and normally distributed with an average of 60 cm and variance of 25 cm2, N(60,5). There is flood in the city if monthly rainfall exceeds 75 cm.
(a)What is the probability of having less than 50 cm?
(b)What is the probability of occurrence of flood?
(c)What is the probability that monthly rainfall exceeds 50 and no flood occurs?
(d)What will be the maximum monthly rainfall if probability of occurrence is 90%?

 

a) 0.02275
b) 0.00135
c) 1 - (0.02275 + 0.00135) = 0.9759 (between extremes a and b).
d) 66.408cm

I haven't taken statistics in 5 years so this could very well be wrong. I used a mean of 60cm, a standard deviation of 5cm (SQRT of 25cm2), and the fact that the data is normally distributed to solve these.