Let c be a constant and consider the density function for the random variable Y a. Find the value of c. b.Find the cumulative distribution function F(y). c.Compute F(2.5) d.Compute P(Y > 2)

Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval. The joint probability mass function of X and Y is as follows: a. What is the value of C? b. Find the marginal probability mass function . c. Find the marginal probability mass function . d. Find u_x . e. Find  u_y. f. Find sigma_x. g. Find  sigma_y. h. Find  cov(x,y). i.  Find rho_xy. j.  E[X+Y] k.  VAR[X+Y] l.  Are X and Y independent? Explain. m.  What is the CDF Fx(x)? n.  What is the CDF Fy(y)?

Let the cumulative distribution function of a distribution is given by: I 3.5. Determine the probability density function f(r) of the distribution.

The data for the joint probability mass function of X and Y (two different measurement systems) aregiven in the table below.a) Calculate the marginal distributions of X and Y and plot them.b) Select one of the Y values from the table and find the conditional probability mass function of X for thatY value you have selected and plot it.c) Show whether X and Y are independent or not.d) Calculate the covariance of (X,Y) i.e. Cov(X,Y).