1. Use the Monte Carlo method to estimate the following: Jo exp(exp(x)) dx this easy version of the Monte Carlo method, uses the law of large numbers: Law of Large Numbers: if {X; } are i.i.d. UNiform on [0, 1], n Σh(X;) → i=1 ["₁ The more complete Monte Carlo method allows to compute h(x)dx = E(h(X)) ["h h(x)f(x)dx = E(h(X)) for other random variebles, not only Uniform. Monte Carlo uses a Markov chain to generate sapling from the "steady state" distribution. See slides attached. In this problem, you are only asked to try the Law of Large Numbers.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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1. Use the Monte Carlo method to estimate the following: o'exp(exp(x)) dx
this easy version of the Monte Carlo method, uses the law of large numbers:
Law of Large Numbers: if {Xi} are i.i.d. UNiform on [0, 1],
n
2 h(X;) →
h(x)dx = E(h(X))
i=1
The more complete Monte Carlo method allows to compute
b
h(x)f(x)dx = E(h(X))
a
for other random variebles, not only Uniform. Monte Carlo uses a Markov chain to generate sapling from the "steady state" distribution. See
slides attached.
In this problem, you are only asked to try the Law of Large Numbers.
2. E(N) where N is defined as follows. Let {U ¡} be i.i.d. Unif(0,1). Define N=min{n: U 1+...+U n
>1}
Calculate N 100 times and then compute the mean. (Also draw the histogram of results)
Repeat this again 10000 times. Comment on your findings. What was the average of your 10000 calculations?
Upload you work (done neatly) here.
Transcribed Image Text:1. Use the Monte Carlo method to estimate the following: o'exp(exp(x)) dx this easy version of the Monte Carlo method, uses the law of large numbers: Law of Large Numbers: if {Xi} are i.i.d. UNiform on [0, 1], n 2 h(X;) → h(x)dx = E(h(X)) i=1 The more complete Monte Carlo method allows to compute b h(x)f(x)dx = E(h(X)) a for other random variebles, not only Uniform. Monte Carlo uses a Markov chain to generate sapling from the "steady state" distribution. See slides attached. In this problem, you are only asked to try the Law of Large Numbers. 2. E(N) where N is defined as follows. Let {U ¡} be i.i.d. Unif(0,1). Define N=min{n: U 1+...+U n >1} Calculate N 100 times and then compute the mean. (Also draw the histogram of results) Repeat this again 10000 times. Comment on your findings. What was the average of your 10000 calculations? Upload you work (done neatly) here.
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