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Chapter 21, Problem 5RQE

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Shape of the binary tree:

A complete binary tree is a binary tree with the property that every node must have exactly two children, and at the last level the nodes should be from left to right.

  • The tree is used to represent more complex relationships in a complex structure.
  • The element of the tree is called as a node and its branches connect the nodes.
  • The shape of the binary tree entirely depends upon the insertion and deletion of nodes in a tree.
    • Mostly the shape depends upon the order in which the nodes are inserted...

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Can you help me solve this problem using Master's Theorem:Solve the recurrence relation f(n) = 3af(n/a) + (n + a)2 with f(1) = 1 and a > 1 byfinding an expression for f(n) in big-Oh notation.
here is example 7.6## Example 7.6 Suppose the sample population is χ 2 (2), which is non-normal but with same variance 4. ▶ Repeat the simulation, but replacing the N(0, 4) samples with χ 2 (2) samples. ▶ Calculate the empirical confidence level.(Empirical confidence level) n <- 20 alpha <- 0.05 UCL <- replicate(1000, expr = { x <- rchisq(n,df=2) (n-1)*var(x)/qchisq(alpha,df=n-1) }) sum(UCL >4) mean(UCL > 4) ## t.test function n <- 20 x <- rnorm(n,mean=2) result <- t.test(x,mu=1) result$statistic result$parameter result$p.value result$conf.int result$estimate
using r language
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