Chapter 1: Problem 19
Find the 25 th percentile of the distribution having pdf \(f(x)=|x| / 4\), where
\(-2
Chapter 1: Problem 19
Find the 25 th percentile of the distribution having pdf \(f(x)=|x| / 4\), where
\(-2
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Get started for freeThere are five red chips and three blue chips in a bowl. The red chips are numbered \(1,2,3,4,5\), respectively, and the blue chips are numbered \(1,2,3\), respectively. If two chips are to be drawn at random and without replacement, find the probability that these chips have either the same number or the same color,
List all possible arrangements of the four letters \(m, a, r\), and \(y .\) Let \(C_{1}\) be the collection of the arrangements in which \(y\) is in the last position. Let \(C_{2}\) be the collection of the arrangements in which \(m\) is in the first position. Find the union and the intersection of \(C_{1}\) and \(C_{2}\).
Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) their product is even.
Suppose \(\mathcal{D}\) is a nonempty collection of subsets of \(\mathcal{C}\). Consider the collection of events $$ \mathcal{B}=\cap\\{\mathcal{E}: \mathcal{D} \subset \mathcal{E} \text { and } \mathcal{E} \text { is a } \sigma \text { -field }\\} $$ Note that \(\phi \in \mathcal{B}\) because it is in each \(\sigma\) -field, and, hence, in particular, it is in each \(\sigma\) -field \(\mathcal{E} \supset \mathcal{D}\). Continue in this way to show that \(\mathcal{B}\) is a \(\sigma\) -field.
Suppose there are three curtains. Behind one curtain there is a nice prize, while behind the other two there are worthless prizes. A contestant selects one curtain at random, and then Monte Hall opens one of the other two curtains to reveal a worthless prize. Hall then expresses the willingness to trade the curtain that the contestant has chosen for the other curtain that has not been opened. Should the contestant switch curtains or stick with the one that she has? To answer the question, determine the probability that she wins the prize if she switches.
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