The probability density function of a random variable W is given by:
$$f(w) = kw^4e^w$$
for $2.002\leq w\leq 3.543$
a. Find constant $k$
b. Compute for $E(W)$
c. Compute for $Var(W)$
d. What is the probability that W will have a value greater than 2.5?
I have answered letter (a) for this no. however I'm not sure if I got the right answer for it that's why I havent answered the next letters. I used integration by parts to integrate the fxn and equated it to 1 since one of the theorems for continuous pdf's states that the integral of the fxn should be equal to 1. I got k = 4.074487547x10^-4 and the integral is $e^w(w^4-4w^3+12w^2-24w+24)$. Did I get the correct answer? If not, please indicate why I got it wrong. Also, should I use the substitution rule for indefinite integrals for letter (d)? Thanks!