easy Probability
A release-checked easy problem for training Markov/Chebyshev Inequalities, Exponential/Gamma, Limit Theorems, Continuous Random Variables.
Jon loves cheese. He decides to make $100$ blocks of cheese. The distribution of the weight (in grams) of each block he makes follows IID $\exponential{1/250}$ distribution. For consistency, let $W_i$ denote the weight of the $i$th block of cheese, and $T_{100}$ represent the total weight of the $100$ blocks of cheese. Using Markov's Inequality, find an upper bound for $\mathbb{P}[T_{100} > 26000]$.
This Probability problem is tagged Markov/Chebyshev Inequalities, Exponential/Gamma, Limit Theorems, Continuous Random Variables. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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