MATLAB: Plotting standard normal rvs

standard normal rvs

I'm trying to determine the plot of the standard normal (for n=10) and plot it. Can I do this by using y=1/2*erfc(-x/sqrt(2)) or can I use y =1/sqrt(2*pi*sigma2) * exp(-(x-mu).^2 /(2 * sigma2));

Thank you

Best Answer

If you have the Statistics Toolbox, then this is extremely easy, just using the normpdf function which encodes the formula for you.

MU    = 10;
SIGMA = 1;
x = 5 : 0.01 : 15;
y = normpdf(x,MU,SIGMA)
figure
plot(x,y)

If you don't have the toolbox, then just use

y =1./sqrt(2*pi*SIGMA) * exp(-(x-MU).^2 /(2 * SIGMA));

instead.

Related Solutions

MATLAB: How to use lognrnd

It is common to say that X is lognormally distributed with parameters mu and sigma if it has the pdf

f(x) = 1/(x*sigma*sqrt(2*pi))*exp(-(log(x)-mu)^2/(2*sigma^2))

If you now calculate the pdf of log(X), you'll see that it equals

g(y) = 1/(sigma*sqrt(2*pi))*exp(-(y-mu)^2/(2*sigma^2))

Thus log(X) is normally distributed with parameters mu and sigma.

To calculate 10^6 random numbers from a lognormally distributed random variable with mean 14 and standard deviation 7, your code from above is correct.

MATLAB: Generate A Sequence of 25 Independent Bernoulli RVs with p = .8

If you are not too concerned about efficiency, and I suspect that you are not, you could use a while loop.

p = 0.8;
Y(35,1) = false; % Create a column vector of 35 zeros
ones_count = 0;
i = 1;
while (ones_count < 25)
  Y(i) = (rand <= p);
  ones_count = ones_count + Y(i);
  i = i + 1;
end
Y(i : end) = []; % Clear unused part of vector. A misleadingly simple operation.
number_of_rands = length(Y);

Of course, the initial allocation of 35 elements for Y may not be sufficient, but that is unlikely. Even if not sufficient, Matlab will create the new elements for you, albeit inefficiently, when you do Y(i) = ... for i > 35. In any case writing:

Y(i:end) = [];

Makes your code inefficient, so no point worrying about efficiency.

Best Answer

Related Solutions

MATLAB: How to use lognrnd

MATLAB: Generate A Sequence of 25 Independent Bernoulli RVs with p = .8

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