Solution: Treap, also known as random binary search tree, Random binary tree and Uniform spanning tree are all random tree. Random tree is a tree formed by a random process of addition and deletion of nodes. AVL tree is a self – balanced binary search tree.

Solution: The randomized binary search tree is formed by the stochastic process. The stochastic process or also called random process is a mathematical tool or object including random variables.

Solution: As there are 3 numbers (1, 3, 2) so total of 6 combinations can be formed using three numbers but Since (2, 1, 3) and (2, 3, 1) are same so in total there are 5 randomized binary search tree that can be formed.

Solution: The expected value of depth of a node that is for a node a, the expected value of length of path from root to node a is found to be at most 2 log n + O(1).

Solution: Although it is difficult to find the length of the longest path in randomized binary search tree, but it has been found that the longest length is around 4.311 log x.

Solution: The longest path in a randomized binary search tree, but it has been found that the longest length is around 4.311 log x for node x. This is also equal to 1/β log x where β lies in the range (0, 1).

Solution: In a random mathematical model, the expected value of number of leaves in a randomized binary search tree is found to be exactly (n + 1)/3 using probability.

Solution: Treap is a type of data structure which is a combination of binary tree and heap. It is an example of a randomized binary search tree. It stores value in pairs.

Solution: Catalan number is a sequence of natural number that is used in counting problem. Hence it is found that the selecting off a tree uniformly at random is reciprocal of Catalan number.

Solution: Beta distribution can be used using a different shape to generate a randomized binary search tree to create a special type of tree known as a botanical tree.