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Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________
Correct answer is '4.25'. Can you explain this answer?
Verified Answer
Let T be a full binary tree with 8 leaves. (A full binary' tree ha...
A Full binary tree with 8 leaves, the number of ways in which 2 leaves independently can be chosen is 8 * 8= 64
64 pairs of leaves exists
In this, 8 pairs will at distance 0 from each other
8 pairs will be at distance 2 from each others (children of the same parent)
16 pairs will be at distance 4 from each other
32 pairs will be at distance 6 from each other
Hence total distance is 8 * 0 + 8 * 2 + 16 * 4 + 32 * 6 = 272
Expected distance is 272/64 = 4.25
64 pairs of leaves exists
In this, 8 pairs will at distance 0 from each other
8 pairs will be at distance 2 from each others (children of the same parent)
16 pairs will be at distance 4 from each other
32 pairs will be at distance 6 from each other
Hence total distance is 8 * 0 + 8 * 2 + 16 * 4 + 32 * 6 = 272
Expected distance is 272/64 = 4.25
Most Upvoted Answer
Let T be a full binary tree with 8 leaves. (A full binary' tree ha...
Introduction:
We are given a full binary tree with 8 leaves, and we need to find the expected value of the distance between two randomly chosen leaves from the tree.
Understanding the problem:
To solve this problem, we first need to understand what a full binary tree is. In a full binary tree, every level is completely filled except for the last level, which is filled from left to right.
Approach:
To find the expected value of the distance between two randomly chosen leaves, we can consider all possible pairs of leaves and calculate the distance between each pair. Then, we can take the average of all these distances to find the expected value.
Calculating the distance:
In a full binary tree, the distance between two leaves can be calculated by counting the number of edges in the path between them. Since each level in a full binary tree has twice the number of nodes compared to the previous level, the distance between two leaves at the same level is always the same. Therefore, we only need to consider the distances between leaves at different levels.
Counting the distances:
Let's consider all the possible distances between leaves in the full binary tree:
- Distance 1: There are 4 pairs of leaves that are adjacent to each other at the same level. The distance between these pairs is 1.
- Distance 2: There are 2 pairs of leaves that are one level apart. The distance between these pairs is 2.
- Distance 3: There are 1 pair of leaves that are two levels apart. The distance between this pair is 3.
- Distance 4: There are 1 pair of leaves that are three levels apart. The distance between this pair is 4.
Calculating the expected value:
To calculate the expected value, we need to take the average of all the distances calculated above, weighted by the probability of selecting each pair of leaves.
- Probability of selecting a pair of leaves at distance 1: 4/28 = 1/7
- Probability of selecting a pair of leaves at distance 2: 2/28 = 1/14
- Probability of selecting a pair of leaves at distance 3: 1/28
- Probability of selecting a pair of leaves at distance 4: 1/28
Now we can calculate the expected value using the formula:
Expected value = (1/7 * 1) + (1/14 * 2) + (1/28 * 3) + (1/28 * 4) = 4.25
Therefore, the expected value of the distance between two randomly chosen leaves in the full binary tree is 4.25.
We are given a full binary tree with 8 leaves, and we need to find the expected value of the distance between two randomly chosen leaves from the tree.
Understanding the problem:
To solve this problem, we first need to understand what a full binary tree is. In a full binary tree, every level is completely filled except for the last level, which is filled from left to right.
Approach:
To find the expected value of the distance between two randomly chosen leaves, we can consider all possible pairs of leaves and calculate the distance between each pair. Then, we can take the average of all these distances to find the expected value.
Calculating the distance:
In a full binary tree, the distance between two leaves can be calculated by counting the number of edges in the path between them. Since each level in a full binary tree has twice the number of nodes compared to the previous level, the distance between two leaves at the same level is always the same. Therefore, we only need to consider the distances between leaves at different levels.
Counting the distances:
Let's consider all the possible distances between leaves in the full binary tree:
- Distance 1: There are 4 pairs of leaves that are adjacent to each other at the same level. The distance between these pairs is 1.
- Distance 2: There are 2 pairs of leaves that are one level apart. The distance between these pairs is 2.
- Distance 3: There are 1 pair of leaves that are two levels apart. The distance between this pair is 3.
- Distance 4: There are 1 pair of leaves that are three levels apart. The distance between this pair is 4.
Calculating the expected value:
To calculate the expected value, we need to take the average of all the distances calculated above, weighted by the probability of selecting each pair of leaves.
- Probability of selecting a pair of leaves at distance 1: 4/28 = 1/7
- Probability of selecting a pair of leaves at distance 2: 2/28 = 1/14
- Probability of selecting a pair of leaves at distance 3: 1/28
- Probability of selecting a pair of leaves at distance 4: 1/28
Now we can calculate the expected value using the formula:
Expected value = (1/7 * 1) + (1/14 * 2) + (1/28 * 3) + (1/28 * 4) = 4.25
Therefore, the expected value of the distance between two randomly chosen leaves in the full binary tree is 4.25.
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Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer?.
Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer?.
Solutions for Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer?, a detailed solution for Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? has been provided alongside types of Let T be a full binary tree with 8 leaves. (A full binary' tree has every level full.) Suppose two leaves a and b of T are chosen uniformly and independently at random. The expected value of the distance between a and b in T (i.e., the number of edges in the unique path between a and b) is (rounded off to 2 decimal places) _________Correct answer is '4.25'. Can you explain this answer? theory, EduRev gives you an
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