(Solved): please show all work by hand c: For the distribution (given in equation form below): a) Calculate th ...

c: For the distribution (given in equation form below): a) Calculate the value of $$k$$ (hint: what must be true about the total probability for any probability distribution covering all possible value of $$x$$ ?). b) Calculate the distribution mean $$?$$ and variance $${?}^2$$. c) Sketch the probability distribution and the cumulative probability distribution. The cumulative probability distribution is the sum of probabilities from the least value to the greatest, so for each value of $$x$$, what is the "accumulated" proabability: for $$x=1$$, the probability is as stated, for $$x=2$$ you are calculating the $$p(x?2)$$, for $$x=3$$ calculate $$p(x?3)$$, etc. $$p(x)=?\begin{array}{cc}4k,& x=1\\ 10k,& x=2\\ 6k,& x=3\end{array}$$ Problem courtesy of textbook