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If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.
Correct answer is '12'. Can you explain this answer?
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If a random variable follows Poisson distribution with mean 3, then V...
Given mean = 3
⇒ Variance = 3 (∵ X follows Poisson distribution)
∴ V(2X + 5) = 4V (X)
= 4 x 3 =12
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If a random variable follows Poisson distribution with mean 3, then V...
Calculating V(2X + 5) for a Poisson distribution with mean 3:
1. Understanding the Poisson distribution:
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space. It is often used to model the number of events that occur within a specific time period.
The Poisson distribution is characterized by a single parameter, λ (lambda), which represents the average rate of occurrence of the events. In this case, the mean is given as 3, so λ = 3.
2. Finding the mean and variance of 2X:
Given that X follows a Poisson distribution with mean 3, we need to find the mean and variance of 2X.
The mean of 2X can be calculated as:
E(2X) = 2 * E(X) = 2 * 3 = 6
The variance of 2X can be calculated as:
V(2X) = (2^2) * V(X) = 4 * V(X)
3. Calculating the variance of X:
To calculate the variance of X, we need to use the formula:
V(X) = λ
Therefore, V(X) = 3.
4. Substituting the values:
We can now substitute the values we have found into the equation for V(2X):
V(2X) = 4 * V(X) = 4 * 3 = 12
5. Conclusion:
Therefore, the variance of 2X + 5, for a Poisson distribution with mean 3, is 12.
1. Understanding the Poisson distribution:
The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space. It is often used to model the number of events that occur within a specific time period.
The Poisson distribution is characterized by a single parameter, λ (lambda), which represents the average rate of occurrence of the events. In this case, the mean is given as 3, so λ = 3.
2. Finding the mean and variance of 2X:
Given that X follows a Poisson distribution with mean 3, we need to find the mean and variance of 2X.
The mean of 2X can be calculated as:
E(2X) = 2 * E(X) = 2 * 3 = 6
The variance of 2X can be calculated as:
V(2X) = (2^2) * V(X) = 4 * V(X)
3. Calculating the variance of X:
To calculate the variance of X, we need to use the formula:
V(X) = λ
Therefore, V(X) = 3.
4. Substituting the values:
We can now substitute the values we have found into the equation for V(2X):
V(2X) = 4 * V(X) = 4 * 3 = 12
5. Conclusion:
Therefore, the variance of 2X + 5, for a Poisson distribution with mean 3, is 12.
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If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer?
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If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer?.
If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a random variable follows Poisson distribution with mean 3, then V(2X + 5) = _________.Correct answer is '12'. Can you explain this answer?.
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