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3 problems match “expectation”. Clear

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1. Expected consecutive pairs in a subset ●●○○○ 20 ptsA 25-element subset is chosen uniformly at random from $\{1,2,\ldots,100\}$. Find the expected number of pairs $(i,i+1)$ of consecutive integers for which both $i$ and $i+1$ lie in the subset.
2. Mean of a normal distribution ●●○○○ 20 ptsLet $X$ be normally distributed. Given that $P(-3<X<-1)=P(3<X<5)$, find the expectation $E(X)$.
3. Expected count of numbers exceeding a neighbor ●●●○○ 50 ptsThe numbers $1$ to $10$ are written in a circle in a random order. Find the expected number of numbers that are at least $2$ larger than at least one of their two adjacent numbers. Round to two decimal places.