Write the process to find a parameter using maximum likelihood method.a. Estimate the parameter p of the geometric distribution.b. Using maximum likelihood method, estimate of θ in the density function

To find a parameter using the maximum likelihood method, follow these steps:

a. Estimate the parameter p of the geometric distribution:

1. Define the likelihood function: The likelihood function represents the probability of observing the given data for different values of the parameter p.
2. Take the derivative of the likelihood function with respect to p.
3. Set the derivative equal to zero and solve for p to find the maximum likelihood estimate (MLE) of p.
4. Check the second derivative of the likelihood function to ensure that the MLE is a maximum.

b. Estimate θ in the density function using the maximum likelihood method:

1. Define the likelihood function: The likelihood function represents the probability of observing the given data for different values of the parameter θ.
2. Take the derivative of the likelihood function with respect to θ.
3. Set the derivative equal to zero and solve for θ to find the maximum likelihood estimate (MLE) of θ.
4. Check the second derivative of the likelihood function to ensure that the MLE is a maximum.

By following these steps, you can estimate the parameters using the maximum likelihood method.