In Week 10- Thursdays class, we considered the following example: The time (measured in hours) between infection and the display of symptoms for streptococcal sore throat is a random variable, T, whose probability density function can be approximated by the function f(t)=115,676 t 2 e 0.05t 0 t 1500 otherwise. (a) Set up an expression for = E[T], and evaluate your expression with the help of an online integration tool such as WolframAlpha. Give your answer to 6 decimal digits. You MUST include the integral you put into the online tool in your solution. (b) Set up an expression for the variance 2= Var[T], and evaluate your expression with the help of an online integration tool such as WolframAlpha. Give your answer to 4 decimal digits. You MUST include the integral you put into the online tool in your solution. (c) Use integration by parts to derive a reduction formula for integrals of the form t n e at dt (n 1), where a is any positive constant. Your reduction formula should express this integral in terms of n, a, function(s) of t, and the reduced integral t n1 e at dt .(d) Use your reduction formula to compute the probability that the time between infection and display of symptoms will be within one standard deviation of the mean, i.e. between and +.