Stat 514

Exercise

Suppose that a particle of initial size y₀ is subjected to repeated impacts, that on each impact a proportion, X_i , of the particle is left, and that the X_i are modeled as independent random variables having the same distribution (iid). After the first impact the size of the particle is Y₁= X₁y₀, and after n impacts the size is:

Y_n = X_nX_n-1...X₂X₁y₀

We are interested in EY_n and in P( Y_n < 3), Following are data from an experiment in which a particle was subjected to 50 impacts. Using the data, estimate EY_n , P( Y_n < 3), and the standard error of the estimate of EY_n. Let the value of y₀ be 10,000,000 units.

The data set are in the html form so that you can copy and paste.