In recent times, likelihood functionexponential distribution has become increasingly relevant in various contexts. 18.05 S22 Reading 10b: Maximum Likelihood Estimates. We have casually referred to the exponentialdistribution or the binomial distribution or the normal distribution. In fact the exponential distribution exp() is not a single distribution but rather a one-parameter family of distributions. Calculating maximum-likelihood estimation of the exponential ....
The likelihood function misses an $i$ in the third block of equations. The power should be $-\lambda x_i$ Exponential distribution - Wikipedia. A common predictive distribution over future samples is the so-called plug-in distribution, formed by plugging a suitable estimate for the rate parameter λ into the exponential density function.
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