A3. Let X and Y be independent random variables with probability density functions fx(x) %3D e, >0 and 0 otherwise; fr(4) 2e-", y >0 and 0 otherwise. %3D (a) Derive the probability density function of Z, = min(X, Y); (b) Derive the probability density function of Zz = y.

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According to a study conducted by a statistical​ organization, the proportion of people who are satisfied with the way things are going in their lives is 0.88. Suppose that a random sample of 100 people is obtained. Complete parts​ (a) through​ (e) below. ​(a) Suppose the random sample of 100 people is​ asked, "Are you satisfied with the way things are going in your​ life?" Is the response to this question qualitative or​ quantitative? Explain.     A. The response is qualitative because the responses can be classified based on the characteristic of being satisfied or not.   B. The response is quantitative because the number of people satisfied can be counted.   C. The response is quantitative because the responses can be classified based on the characteristic of being satisfied or not.   D. The response is qualitative because the number of people satisfied can be counted. ​(b) Explain why the sample​ proportion, p​, is a random variable. What is the source…