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(a) grain/needle throws? How would you use i.i.d. random variables to model the location of the (b) Write your estimate of T in terms of these i.i.d. random variables. (c) Prove that under the i.i.d. model, your estimate of 7 converges in probability to T.

(a) grain/needle throws? How would you use i.i.d. random variables to model the location of the (b) Write your estimate of T in terms of these i.i.d. random variables. (c) Prove that under the i.i.d. model, your estimate of 7 converges in probability to T.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter13: Division Of Decimal Fractions
Section: Chapter Questions
Problem 17A: The bolt in Figure 136 has 7.7 threads. Determine the pitch to 3 decimal places. All dimensions are...
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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
Transcribed Image 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
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.
Transcribed Image 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.
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