that can piece through the paper the idea is that you throw very small items of which the shape can be ignored). After many throws, you count the proportion of grains/needles that end up inside the...

Show work

Extracted text: that can piece through the paper the idea is that you throw very small items of which the shape can be ignored). After many throws, you count the proportion of grains/needles that end up inside the circle, multiply it by 4, and that's your estimate of T. An illustration is as follows: (a) How would you use i.i.d. random variables to model the location of the grain/needle throws? (b) Write your estimate of T in terms of these i.i.d. random variables. Prove that under the i.i.d. model, your estimate of 7 converges in probability to T.


Extracted text: Question 6 One way to estimate 7 is to do the following. Suppose you draw a square and its inscribed circle on a piece of paper. Then you randomly throw small grains one by one (or needles 3