课程: Probability Foundations for Data Science

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MLE for normal distribution

MLE for normal distribution

课程: Probability Foundations for Data Science

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MLE for normal distribution

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- [Instructor] Let's wrap up maximum likelihood estimation by using it with the normal distribution. Remember, the normal distribution is used to model many real valued random variables that have a symmetric bell curve. If you remember in this case, the expectation of X is going to be equaling mu and the variance of X is going to be equaling sigma squared. The following equation is the probability density function for the normal distribution. So you have your function for x and mu and sigma squared, and this will equal to 1 divided by the square root of 2 multiplied by pi multiplied by sigma squared. And then you multiply all this by e to the -x minus mu squared, divided by 2 multiplied by sigma squared. Like before, use the steps you learn to find the maximum likelihood estimate for the expectation and the variance of your normal distribution. First, define your likelihood function. Suppose you have a sample of values of X equal to x1 to xn of n independent and identically…

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