Question
Answer and Explanation
To plot the Probability Mass Function (PMF) given parameters `n` and `p` in MATLAB, you'll be dealing with a binomial distribution. Here’s how you can achieve this:
1. Define Parameters:
- Start by defining your `n` (number of trials) and `p` (probability of success on each trial) values.
2. Generate x-values:
- Create a vector of x-values representing the possible outcomes of the binomial distribution. This vector will usually range from 0 to `n`.
3. Calculate PMF:
- Use the binopdf function to compute the PMF values for the given x-values, `n` and `p`. This function computes the probability of obtaining exactly 'k' successes in 'n' independent trials.
4. Plot the PMF:
- Finally, plot the x-values against the corresponding PMF values. Using `stem` is great for PMFs as it displays discrete values well.
5. Complete MATLAB code:
% Define parameters n and p
n = 10; % Number of trials
p = 0.3; % Probability of success
% Generate x-values (possible outcomes)
x = 0:n;
% Calculate the PMF using binopdf function
pmf = binopdf(x, n, p);
% Plot the PMF using stem plot
stem(x, pmf, 'filled', 'MarkerFaceColor', 'blue');
xlabel('Number of Successes (k)');
ylabel('Probability P(X=k)');
title(['Binomial PMF with n=' num2str(n) ' and p=' num2str(p)]);
grid on;
6. Code Explanation:
- The script first defines `n` (number of trials) and `p` (probability of success). The x-values range from 0 to n. It then calculates the probability mass function `pmf` using MATLAB's built-in binopdf function, which takes the x values, number of trials `n`, and probability of success `p` as input. Finally, the stem function is used to plot these probabilities against the corresponding successes, and the graph is labeled to be understandable.
7. Considerations:
- Remember to label your axes and title your plot so that the graph is properly understood. Adjust `n` and `p` to generate the desired distribution.
By following these instructions, you can effectively generate and visualize the PMF of a binomial distribution using MATLAB.