Question 11: Determine and report the mean of the 60 simulated rainfall duration values. How does this value compare to the theoretical expected value of the Exponential random variable? It turns out that statisticians know a lot about the Exponential distribution. Once you choose to model a random variable with an Exponential distribution, you can answer all sorts of questions about that variable related to probability. Take, for example, the question, "What is the probability that a randomly chosen rainfall event in Corvallis in/nExponential distribution. Once you choose to model a random variable with an Exponential distribution, you can answer all sorts of questions about that variable related to probability. Take, for example, the question, "What is the probability that a randomly chosen rainfall event in Corvallis in January is longer than 4 hours?" If we assume that rainfall duration is Exponentially distributed, we can find this theoretical probability by using the pexp() function in R. 1-pexp (q = 4, rate = 1/3) Note that the function pexp() gives the area under the Exponential curve below a given value, q, with a given rate (X) parameter. Since we're interested in the probability that rainfall duration is greater than 4 hours, we have to take one minus that probability. Assuming an Exponential distribution has allowed us to calculate a theoretical probability. If we want to calculate the probability empirically from our simulated data we simply need to determine how/nto calculate the robabinity empirically fontour simulated data, we simply need to determine how many observations fall above 4, then divide this number by the total sample size: df %>% filter (sim_exp > 4) %>% summarise (proportion = n()/nrow(df))

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