Calculating a probability from a pdf.

• Dec 20th 2010, 08:59 AM
DanBrown100
Calculating a probability from a pdf.
Need help with a question guys, any help will be most appreciated.

The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula:

x = 3 + ln(y/1-y)

Determine the probability of breakdown for 1, 3 and 10 years.

It has got me a bit stumped guys so any help would be most appreciated.

Thanks
• Dec 20th 2010, 11:06 AM
emakarov
Quote:

The age of a machine, x, in years, is related to the probability of breakdown, y, by the formula:

x = 3 + ln(y/1-y)

Determine the probability of breakdown for 1, 3 and 10 years.
For example, $\displaystyle 10=3+\ln(y/(1-y))$; we need to find y. Then $\displaystyle \ln(y/(1-y))=7$. Raise $\displaystyle e$ to both sides keeping in mind that $\displaystyle e^{\ln a}=a$ for all $\displaystyle a>0$. This will give you a linear equation on y. Formally, after finding y, you must check that $\displaystyle y/(1-y) > 0$ to make sure that $\displaystyle \ln(y/(1-y))$ exists because when one raises e to both sides of an equation, one can acquire spurious roots.