Let X and Y be two independent, exponentially distributed random variables with parameters ,lambda and mu, respectively.

Question

1.Find P(X<=Y)
2. Let Z=1/(1+X) for 0<z<1 find f_z(z)

For 1 i have :
lambda/(mu+lambda)

for 2 I have:

f_z(z) = lambda*(e^(-lambda*((1-z)/z)))*1/z^2

Could you please guys double check? thanks in advance