A perfect coin should produce heads and tails with equal probability. If we assign the number 0 toheads and the number 1 to tails, then we can mimic such a perfect coin in Matlab. Specifically, we cangenerate N “coin flips” in Matlab by doing x= (rand(N, 1) < 0.5 );, where becomes an array of zeros(“heads") and ones (“tails"). For a perfect coin, the mean of that array should be exactly 0.5. Experimentwith how many coin flips you need to get close to this value. Specifically, generate N = 16 coin flips and compute the sample mean (in Matlab, mean(x)). Then generate N = 32 coin flips and compute a newmean. Repeat this process for N = 2k for k = 4,5,…,26. For each value of N, the error in your computedmean is the absolute value of the computed sample mean and 0.5 (i.e., error = abs( mean(x) - 0.5 );). Plot this error vs N. Try linear and logarithmic axes. What patterns do you see?

Question

A perfect coin should produce heads and tails with equal probability. If we assign the number 0 toheads and the number 1 to tails, then we can mimic such a perfect coin in Matlab. Specifically, we cangenerate N “coin flips” in Matlab by doing x= (rand(N, 1) < 0.5 );, where becomes an array of zeros(“heads") and ones (“tails"). For a perfect coin, the mean of that array should be exactly 0.5. Experimentwith how many coin flips you need to get close to this value. Specifically, generate N = 16 coin flips and compute the sample mean (in Matlab, mean(x)). Then generate N = 32 coin flips and compute a newmean. Repeat this process for N = 2k for k = 4,5,…,26. For each value of N, the error in your computedmean is the absolute value of the computed sample mean and 0.5 (i.e., error = abs( mean(x) - 0.5 );). Plot this error vs N. Try linear and logarithmic axes. What patterns do you see?

This question is on Chegg, if anyone has an account, could you please screenshot it? If possible.

Answer 1

As an AI, I don't have access to external websites like Chegg or the ability to take screenshots. However, I can help you understand how to approach this problem.

To answer this question and plot the error versus N, you would need to follow these steps in MATLAB:

1. Initialize an empty array to store the errors, e.g., `errors = []`.
2. Define a range of values of N, such as `N_values = [16, 32, 64, 128, ..., 2^26]`.
3. Use a loop to iterate through each value of N:
- Generate N coin flips using the code `x = (rand(N, 1) < 0.5);`.
- Compute the sample mean using the code `sample_mean = mean(x)`.
- Compute the error using the code `error = abs(sample_mean - 0.5)`.
- Append the error to the `errors` array using `errors = [errors, error]`.

4. Once the loop is complete, you will have an array of errors for each value of N.
5. Plot the error versus N using the `plot` function in MATLAB, e.g., `plot(N_values, errors)`.

To plot the error versus N with both linear and logarithmic axes, you can use the `plot` function combined with the `semilogx` function in MATLAB. The `plot` function will give you a linear plot, while the `semilogx` function will give you a logarithmic plot on the x-axis.

Here's an example code snippet to help you get started:

```matlab
errors = [];
N_values = 2.^(4:26);

for N = N_values
x = (rand(N, 1) < 0.5);
sample_mean = mean(x);
error = abs(sample_mean - 0.5);
errors = [errors, error];
end

% Linear plot
plot(N_values, errors);
title('Error vs N - Linear Axis');
xlabel('N');
ylabel('Error');

% Logarithmic plot
semilogx(N_values, errors);
title('Error vs N - Logarithmic Axis');
xlabel('Log(N)');
ylabel('Error');
```

Running this code will generate two plots, one with a linear x-axis and another with a logarithmic x-axis. By analyzing these plots, you can observe any patterns in the error as N increases.