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Let X be a random variable which is uniformly chosen from the set of positive odd numbers
less than 100. The expectation E[X]is __________.
less than 100. The expectation E[X]is __________.
Correct answer is '50'. Can you explain this answer?
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Let X be a random variable which is uniformly chosen from the set of p...
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Let X be a random variable which is uniformly chosen from the set of p...
Understanding the Problem:
We are given that the random variable X represents positive odd numbers less than 100, and it is uniformly chosen from this set. We need to find the expectation E[X].
Solution:
To find the expectation E[X], we need to compute the average value of X by summing up all the possible values of X and dividing by the total number of values.
Step 1: Finding the set of positive odd numbers less than 100:
The set of positive odd numbers less than 100 can be represented as {1, 3, 5, ..., 97, 99}.
Step 2: Finding the total number of values:
The total number of values in the set can be calculated by finding the number of odd numbers between 1 and 99 inclusive. This can be done by subtracting the first odd number from the last odd number and dividing by 2, then adding 1.
Total number of values = (99 - 1) / 2 + 1 = 50.
Step 3: Finding the sum of all values:
To find the sum of all values, we can use the formula for the sum of an arithmetic series. The formula is given by:
Sum = (n/2)(first term + last term), where n is the number of terms.
In this case, the first term is 1 and the last term is 99. Substituting these values into the formula, we get:
Sum = (50/2)(1 + 99) = 25(100) = 2500.
Step 4: Finding the expectation:
Finally, we can find the expectation E[X] by dividing the sum of all values by the total number of values.
E[X] = Sum / Total number of values = 2500 / 50 = 50.
Therefore, the expectation E[X] is equal to 50.
We are given that the random variable X represents positive odd numbers less than 100, and it is uniformly chosen from this set. We need to find the expectation E[X].
Solution:
To find the expectation E[X], we need to compute the average value of X by summing up all the possible values of X and dividing by the total number of values.
Step 1: Finding the set of positive odd numbers less than 100:
The set of positive odd numbers less than 100 can be represented as {1, 3, 5, ..., 97, 99}.
Step 2: Finding the total number of values:
The total number of values in the set can be calculated by finding the number of odd numbers between 1 and 99 inclusive. This can be done by subtracting the first odd number from the last odd number and dividing by 2, then adding 1.
Total number of values = (99 - 1) / 2 + 1 = 50.
Step 3: Finding the sum of all values:
To find the sum of all values, we can use the formula for the sum of an arithmetic series. The formula is given by:
Sum = (n/2)(first term + last term), where n is the number of terms.
In this case, the first term is 1 and the last term is 99. Substituting these values into the formula, we get:
Sum = (50/2)(1 + 99) = 25(100) = 2500.
Step 4: Finding the expectation:
Finally, we can find the expectation E[X] by dividing the sum of all values by the total number of values.
E[X] = Sum / Total number of values = 2500 / 50 = 50.
Therefore, the expectation E[X] is equal to 50.
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Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer?
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Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer?.
Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let X be a random variable which is uniformly chosen from the set of positive odd numbersless than 100. The expectation E[X]is __________.Correct answer is '50'. Can you explain this answer?.
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