(Solved):   I need answers as quick as possible. QUESTION 1 (30 Marks) a) A continuous random variabl ...

 

I need answers as quick as possible.

QUESTION 1 (30 Marks) a) A continuous random variable X has probability density function f(x) Show this EX+)= a(X) + b where 'a' and 'b' are constants. 13 marks) X by Consider the following probability density function of the random variable X. 13 (= 0, otherwise f') = 3(1) ". *=0,1,2,3,4. Determine the probability generating function of the random variable X. 3 marks 13 marks) Using your answer to b), determine the mean of x. e) A discrete random variable X has the following probability density function 1x) = (x+1), x=0,2,4,6 0. otherwise [5 marks! Check if Chebychey's Inequality holds true for the following probability P={x+423 5 (d) Available records indicate that the chances of an open-air kiosk operator making a gross profit of at least £400 in a week e 40%. Six weeks are picked at random.