urgent hw....do help....probability densities
Hi i have the following problems as HW.......try to help me......urgent.......
1) If X and Y have a bivariate normal distribution and U=X+Y and V=X-Y find an expression for the correlation coefficient of U and V.
2)If X has an exponential distribution,show that
P(X >= t + T \ X >= T) = P(X >= t)
this property of an exponential random variable parallels that of a geometric random variable as [P(X = x+n \ X > n)] = P (X=x)
3)If rando variable T is the time to failure of a commercial product and the values of its probability dnsity and distribution function at time "t" are f(t) and F(t), then its failure rate at time t is given by f(t) / 1-F(t). Thus the failure rate at time t is the probability density of failure at time t given that failure does not occur prior to time t.
a) show that if T has an exponential distribution, the failure rate is constant.
b)show that if has a weibull distribution, the failure rate is given by ab t^b-1.