Let Xi, i ∈ N, be independent and identically distributed random variables with values in N0. We transform (‘prune’) the sequence {X1, . . . , Xn}, n ∈ N, of discrete random samples into a sequence {0, 1, 2, . . . , Yn}, n ∈ N, of contiguous random sets by replacing Xn+1 with Yn + 1 if Xn+1 > Yn. We consider the asymptotic behaviour of Yn as n → ∞. Applications include path growth in digital se...

For the next two weeks, I will discuss some of the concepts of random sample which we use very frequently. These are certainly not the central focus of this course, but it is extremely important for all of us to know these concepts. We have to use these ideas throughout this quarter. First we need to know what do we mean by a random sample. Definition: The random variables X1, ..., Xn together ...

For the next two weeks, I will discuss some of the concepts of random sample which we use very frequently. These are certainly not the central focus of this course, but it is extremely important for all of us to know these concepts. We have to use these ideas throughout this quarter. First we need to know what do we mean by a random sample. Definition: The random variables X1, ..., Xn together ...