Density Function

The density function of a continuous variable x is given by f(x) =x; 0≤x<1 and f(x) = 2-x; 1≤x<2 a) Find p(1/2≤x≤3/2) b) Find the median and quartiles of this distribution

mutually exclusive and independent events

Can E and F be both mutually-exclusive and be independent, if they are non-zero probability events. How?

Lease or Buy

I can lease some equipment for $3,000 annually for 6 years or purchasing it for $12,000. If I can invest money at 8% annum, how do I determine which is the better choice finacially?

Determing amount to deposit

If I wanted to set up a trust earning 9% compounded semi-annually so that I could withdraw $10,000 every six months, begining six months from now, for 6 years. How would I determine the amount to deposit now?

Probability

An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15% of individuals known to be cancer-free (false positive). One hundred individuals volunteer to take the test. Of the 100, 60 are known to have the cancer, and 40 are known to be cancer-free. If the test indicates that that one of the individuals, randomly chosen, has the cancer, what is the probability that he or she is actually cancer-free?