1
$\begingroup$

(I have finally edited my question)

I have one equation being compared to a number:

X = any positive real number

X'= (L)+2(Y)+3(Z)

The value of L, Y, and Z are always between 0-1 and its value can change, but it has a probability associated with it. If I use actual numbers, imagine:

L= 0.0-0.3 (90% of the time),
0.0-0.5 (60% of the time),
0.0-0.9 (10% of the time)

Y= 0 or 1 (Y=1, 1% of the time and Y=0, 99% of the time)

Z=
0.00-0.25, 25% of the time
0.25-0.50, 25% of the time
0.50-0.75, 25% of the time
0.75-1.00, 25% of the time

X=2.50

L, Y, Z are independent variables.

I am curious as to how I could calculate the probability of X'>X. Is there a model/equation I can use that can calculate such a thing for me?

Thank you very much everyone!

$\endgroup$
17
  • $\begingroup$ Are L,Y, and Z independent? Also, I think you're going to need more information because depending on the distributions of L,Y, and Z the probability will be different. $\endgroup$
    – VCG
    Aug 20, 2016 at 3:13
  • $\begingroup$ Yes, L, Y, and Z are independent. L,Y and Z follow a normal distribution $\endgroup$
    – TheFermat
    Aug 20, 2016 at 3:26
  • 1
    $\begingroup$ Have you made an attempt on this problem? If the three are independent then you can split their join probabilities. Again the problem is not well specified. A normal distribution is continuous so no single number occurs with probability greater than zero. Are you sure you don't mean that 50% of the time L is below .6? $\endgroup$
    – VCG
    Aug 20, 2016 at 3:28
  • 1
    $\begingroup$ Please don't vandalize your posts. If you edit your question to clarify what you mean, it isn't necessary to create a second post, and it will populate the reopen queue for a re-open vote. The SO model encourages users to edit problematic posts rather than spam the forums $\endgroup$
    – Sycorax
    Aug 23, 2016 at 18:07
  • 1
    $\begingroup$ My comment is predicated on your not having any further information as to the distribution within each interval. Hence my treatment using interval arithmetic cs.utep.edu/interval-comp , which can be automated. II you can specify the distribution within each interval, for instance, uniform, then you can do traditional probability calculations per the links from @whuber nstead of interval arithmetic calculations. The interval approach will have messy conclusions. $\endgroup$ Aug 29, 2016 at 20:38

0

Browse other questions tagged or ask your own question.