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A random process obeys Poisson’s distribution. It is given that the mean of the process is 5. Then the variance of the process is
- a)5
- b)0.5
- c)25
- d)0
Correct answer is option 'A'. Can you explain this answer?
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A random process obeys Poisson’s distribution. It is given that ...
The mean and variance of a Poisson’s distribution are equal. So, if the mean is 5, the variance will also be 5.
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A random process obeys Poisson’s distribution. It is given that ...
Distribution with a rate parameter of λ. This means that the probability of a certain number of events occurring in a given time interval follows the Poisson distribution.
The Poisson distribution is characterized by the following properties:
1. The number of events occurring in non-overlapping intervals are independent of each other.
2. The average rate of events occurring remains constant over time.
3. The probability of more than one event occurring in an infinitesimally small interval is negligible.
4. The probability of an event occurring in a given interval is proportional to the length of the interval.
The probability mass function (PMF) of the Poisson distribution is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where:
- X is the random variable representing the number of events occurring in the interval.
- k is the number of events.
- λ is the rate parameter, which represents the average number of events occurring in the interval.
The mean and variance of the Poisson distribution are both equal to λ.
The Poisson distribution is commonly used to model random events that occur independently over time, such as the arrival of customers at a store, the number of phone calls received in a call center, or the number of accidents on a road. It is also used in various other fields, including physics, biology, and finance, where random processes are encountered.
The Poisson distribution is characterized by the following properties:
1. The number of events occurring in non-overlapping intervals are independent of each other.
2. The average rate of events occurring remains constant over time.
3. The probability of more than one event occurring in an infinitesimally small interval is negligible.
4. The probability of an event occurring in a given interval is proportional to the length of the interval.
The probability mass function (PMF) of the Poisson distribution is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where:
- X is the random variable representing the number of events occurring in the interval.
- k is the number of events.
- λ is the rate parameter, which represents the average number of events occurring in the interval.
The mean and variance of the Poisson distribution are both equal to λ.
The Poisson distribution is commonly used to model random events that occur independently over time, such as the arrival of customers at a store, the number of phone calls received in a call center, or the number of accidents on a road. It is also used in various other fields, including physics, biology, and finance, where random processes are encountered.
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A random process obeys Poisson’s distribution. It is given that the mean of the process is 5. Then the variance of the process isa)5b)0.5c)25d)0Correct answer is option 'A'. Can you explain this answer?
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A random process obeys Poisson’s distribution. It is given that the mean of the process is 5. Then the variance of the process isa)5b)0.5c)25d)0Correct answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A random process obeys Poisson’s distribution. It is given that the mean of the process is 5. Then the variance of the process isa)5b)0.5c)25d)0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A random process obeys Poisson’s distribution. It is given that the mean of the process is 5. Then the variance of the process isa)5b)0.5c)25d)0Correct answer is option 'A'. Can you explain this answer?.
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