Assume we have a large number of particles \(N\) of Strontium. The decay model for Strontium is exponential in that \(\mathbf{P}(T > t) = e^{- \lambda t}\), this states the probability of a an atom surviving until time \(T\).

1. The half-life of a substance is the amount of time it takes for an appreciable amount of the substance to be reduced in half. If the half life of strontium is 28 years what is the decay parameter of the exponential ?
2.  What is the probability Strontium lasts at least 50 years, \(\mathbf{P}(T > 50) \) ?
3. Suppose we have \(5\) radioactive substances, the decay of each of which can be modeled by five exponential random variables \(X_1,…,X_5\) with parameters \(\lambda_1,…,\lambda_5\). Assume the five distributions are independent. What is the pdf for \(\min\{X_1,…,X_5\}\).