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3. Consider the probability density function for a random variable T given below, for 0 c it takes the value 64a/t3. Note that the horizontal and vertical scales on the following plot are different, it is only provided to demonstrate the general nature of the distribution and should not be used to determine any values. a 64a 0 4 (a) What must be the value of a in order for this to be a valid prob- ability density function? Show working to justify your answer. (b) Calculate P(T > 3). (c) Calculate E[T]. (d) Show that Var(7') involves an integral which does not take a finite value