We have a function. t ~ Weibull(alpha, lambda) and c ~ Exponential(beta):

I attached a picture for function.

we know:

p = 0.10, alpha = 1, lambda = 4,

lower t = c, Upper t = Infinite , Lower c = 0, Upper c= Infinite, B or beta=?**

We want to integrate this function for "t" then to "c" and finally with function "Uniroot" solve the equation to find amount of "B or beta".

I write this Code in R-studio:

alpha = 1

lambda = 4

p = 0.10

func1