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Medium · Statistics & Regression · Quant Trader interview question · statistics, mle, exponential-distribution, probability
You are modeling the time between trades for a highly liquid stock using an exponential distribution. You have collected $n$ independent and identically distributed (i.i.d.) observations, $x_1, x_2, ..., x_n$, representing the time intervals between consecutive trades. Assume these observations come from an Exponential distribution with rate parameter $\lambda$, denoted as $Exp(\lambda)$. Determine the Maximum Likelihood Estimator (MLE) for the rate parameter $\lambda$.