Answer to Question #48732 in Statistics and Probability for Tot

Question

1)Let X be a r.v. Uniformly distributed (0, 2), and Y = g(X) = 1/XCompute fY (y). Find
The pdf f_Y(y) b. the CDF F_Y(y).
2)Given the pdf of the r.v X; fX (x) and Y=g(x)=|x|. Find fY in terms of fX (x).
3)Assume that waiting for the 2:00 o’clock bus starts at 2:00 o’clock. Let the actual arrival time in minutes past the 2:00 o’clock is , in which X is an exponential r.v. with parameter τ. Let E be the event that you have waited for 5 minutes without seeing the bus. What is the
conditional pdf of X (the additional time you will wait) given E?.
the conditional probability Y=[x-5], given E ?
4)Let the r.v. Z is Gaussian distributed N~(0,4). Given the event Y={Z>0}. What is
The pdf fZ|Y (z) ?
The expected value E_Z|Y (z|w).
The variance value Var Z|Y (z|w).