Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and... Problem 1.2P: How many outcome sequences are possible ten a die is rolled four times, where we say, for instance,... Problem 1.3P: Twenty workers are to be assigned to 20 different jobs, one to each job. How many different... Problem 1.4P: John, Jim, Jay, and Jack have formed a band consisting of 4 instruments if each of the boys can play... Problem 1.5P: For years, telephone area codes in the United States and Canada consisted of a sequence of three... Problem 1.6P: A well-known nursery rhyme starts as follows: As I was going to St. Ives I met a man with 7 wives.... Problem 1.7P: a. In how many ways can 3 boys and 3 girls sit in a row? b. In how many ways can 3 boys and 3 girls... Problem 1.8P: When all letters are used, how many different letter arrangements can be made from the letters a.... 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![**Problem 2: Joint Probability Density Function**
The continuous random variables \(X\) and \(Y\) have a known joint probability density function, \(f_{XY}(x,y)\), given by
\[
f_{XY}(x,y) =
\begin{cases}
\frac{(x+y)}{8} & \text{for } 0 \leq x \leq 2, 0 \leq y \leq 2 \\
0 & \text{otherwise}
\end{cases}
\]
Define the random variable \(Z\) as \(Z = \min(X, Y)\).
Tasks:
a) Determine the probability density function \(f_Z(z)\) of the random variable \(Z\).
b) Determine the probability \(\Pr\{0.5 < Z \leq 1.5\}\).
c) Determine \(E\{Z\}\) and \(\text{var}\{Z\}\).](https://content.bartleby.com/qna-images/question/9328926a-b343-4d47-8a00-cbd9e6e36ac2/e2d8a220-0d93-42b2-a4cb-888869d99072/izc64mj_processed.jpeg)
