find the 30th percentil of an exponential random variable wi

find the 30th percentil of an exponential random variable with mean 3

Solution

For an exponentially distributed random variable \'x\' cdf is given as
C(x) = P(X<k) = 1 - e^(-yx)        [y is lambda]
mean = 1/y
y = 1/3

P(X<k) = 0.30
C(k) = 0.30
1 - e^(-k/3) = 0.30
e^(-k/3) = 0.70
taking natural log on both sides
k = 1.07