Thread: 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.

Where do I start with this one?


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

Thanks

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, ; we need to find y. Then . Raise to both sides keeping in mind that for all . This will give you a linear equation on y. Formally, after finding y, you must check that to make sure that exists because when one raises e to both sides of an equation, one can acquire spurious roots.