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No. of radio- active atoms decaying in a given interval of time is an example of
- a)Binomial distribution
- b)Normal distribution
- c)Poisson distribution
- d)None
Correct answer is option 'C'. Can you explain this answer?
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No. of radio- active atoms decaying in a given interval of time is an ...
Poisson distribution is a statistical concept that describes the probability of a given number of events occurring in a fixed interval of time or space. It is used to model the number of times that an event occurs in a given time frame, such as the number of defects in a product or the number of customers who arrive at a store.
Explanation:
In this given problem, we are interested in the number of radioactive atoms that decay in a given interval of time. The decay of radioactive atoms is a random process, and the rate of decay is proportional to the number of atoms present. Therefore, the number of decays that occur in a fixed interval of time follows a Poisson distribution.
The Poisson distribution has the following properties:
- It is a discrete probability distribution that ranges from 0 to infinity.
- The mean and variance of the distribution are equal and are denoted by λ.
- The probability of observing k events in a fixed interval of time is given by the formula:
P(k) = (e^(-λ) * λ^k) / k!
where e is the mathematical constant approximately equal to 2.71828.
In the given problem, the number of decays that occur in a fixed interval of time can be modeled by a Poisson distribution with a mean of λ. The probability of observing k decays in the interval is given by the Poisson distribution formula.
Therefore, the correct answer is option C, Poisson distribution.
Explanation:
In this given problem, we are interested in the number of radioactive atoms that decay in a given interval of time. The decay of radioactive atoms is a random process, and the rate of decay is proportional to the number of atoms present. Therefore, the number of decays that occur in a fixed interval of time follows a Poisson distribution.
The Poisson distribution has the following properties:
- It is a discrete probability distribution that ranges from 0 to infinity.
- The mean and variance of the distribution are equal and are denoted by λ.
- The probability of observing k events in a fixed interval of time is given by the formula:
P(k) = (e^(-λ) * λ^k) / k!
where e is the mathematical constant approximately equal to 2.71828.
In the given problem, the number of decays that occur in a fixed interval of time can be modeled by a Poisson distribution with a mean of λ. The probability of observing k decays in the interval is given by the Poisson distribution formula.
Therefore, the correct answer is option C, Poisson distribution.
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Poisson distribution.....
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No. of radio- active atoms decaying in a given interval of time is an example ofa)Binomial distributionb)Normal distributionc)Poisson distributiond)NoneCorrect answer is option 'C'. Can you explain this answer?
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