9. Consider the sample space Ω {1.2.3.4 } (the set of all natural numbers). We want...
7. Consider an experiment whose sample space consists of all positive integer (a.k.a. natural) numbers Z+ 1,2,3, ...J (i.e. choose a random natural number) a) Can you define a probability on Z+? (b) Can you define a probability on Z+ in such a way that any two numbers are equally likely to occur? (c) Along the lines of (b), can you define a probability on the interval [0, 1] in such a way that any two numbers in this interval...
7. Consider an experiment whose sample space consists of all positive integer (a.k.a. natural) numbers Z 1,2,3,...] (i.e. choose a random natural number) (a) Can you define a probability on Z+? (b) Can you define a probability on Z+ in such a way that any two numbers are equally likely to occur? (c) Along the lines of (b), can you define a probability on the interval [0, 1 in such a way that any two numbers in this interval are...
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I need only (d) (e) (g)! !!!
In this project, we want to estimate the value of it through random sampling. First, consider the unit square S = {(x, y)0 SX S1, 0 Sy s 1} and the circle C = {(x, y)/(x-1/2)2+(y-1/2)2 5 1/4} which resides inside the unit square. Suppose that we sample n points from the unit square S, uniformly and independently. Let Xi be 1 if the ith sample falls into the circle C and...