Question

Could somebody double check my answers for this exponential distribution question?

"Melancholy" happens by an exponential distribution on average every 5 months.

a) X~

Ans: X~exp(1/5)

b) Find the probability of "Melancholy" after 4 months

Ans: 0.2e^(-0.2*4) = 0.09

c) Find the 75th percentile for "Melancholy" (for 75% soonest "Melancholy" occasions)

Ans: 0.75 = 1-e^(-0.2*x)
0.25=e^(-0.2x)
ln(0.25)=-0.2x
ln(0.25)/(-0.2)=6.93=x=75th percentile.

Thanks in advance!