Please show work I am confused On a calm day when the wind i

Please show work. I am confused

On a calm day, when the wind is not blowing from any particular direction, the speed of wind gusts (S, in mph) follows a distribution with the following PDF: f(s) = -S/4 e^-S^2/8, where s > 0. Do the following. Give the formula that could be used to find the mean of this random variable. Find the median of this random variable. Find the CDF of this random variable. Find the probability that at a randomly-selected time point, the wind speed will exceed 3 mph. A meterologist claims that the true mean wind speed on a calm day is square root 2 pi. The wind speed on a calm day was measured at randomly selected time points. The observed data are posted at Conduct the appropriate test to determine if the true wind speed is square root 2 pi. Do the following, using the 0.05 level of significance: State the null and alternative hypotheses. Give the mean, standard deviation, and the sample test statistic. Find the P-value. Give your conclusion in an English sentence that relates the results to the context of the problem.

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