Question is in the attachment file.

2. Consider a mixed random variable X with an event space of a single discrete event at x = -(B +1) and the piecewise constant continuous proper probability distribution. 0, r 2+A. The mixed probability density function then follows (here 6() dentotes the Dirac delta function) fx(x) = c(6(x + B+ 1) +rfx(x)), where r is a positive real parameter, and A and B are digits of your 6-digit candidate number ABCDEF. (a) Calculate c such that fX(x) is normalized. (b) Calculate the mean u = E[X] (which will depend on the parameter r). (c) Determine the value of r for which u = 0. (d) Calculate the variance o 2 , for this specific value of r (or in the case of a general r if you prefer). (it is acceptable if you insert r and c from above, without simplifying further. But you need to take care of all integrations that occur.) (e) Start calculating the excess kurtosis, using the definition, and performing all integrations, for the specific value of r found above. (f) Find the cumulative distribution function (CDF). It is sufficient to draw it graphically. (g) Find the median, for the parameters above