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If the standard deviation of a Poisson variate X is 2, what is P (1.5 < X < 2.9)?
- a)0.231
- b)0.158
- c)0.15
- d)0.144
Correct answer is option 'D'. Can you explain this answer?
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If the standard deviation of a Poisson variate X is 2, what is P (1.5 ...
A Poisson distribution only takes on integer values, so it doesn't make sense to ask for the probability of a non-integer value like 1.5. However, we can use the fact that the mean of a Poisson distribution is equal to its standard deviation, which in this case is 2. Therefore, the mean of X is also 2.
We can use the Poisson probability mass function to calculate the probability of any integer value of X. Specifically, the probability of X = k is given by:
P(X = k) = (e^-2 * 2^k) / k!
Using this formula, we can calculate the probability of X taking on any integer value. For example:
P(X = 0) = (e^-2 * 2^0) / 0! = 0.1353
P(X = 1) = (e^-2 * 2^1) / 1! = 0.2707
P(X = 2) = (e^-2 * 2^2) / 2! = 0.2707
P(X = 3) = (e^-2 * 2^3) / 3! = 0.1805
P(X = 4) = (e^-2 * 2^4) / 4! = 0.0903
etc.
Note that the sum of all these probabilities must be equal to 1, since X is a discrete random variable that takes on one of these integer values.
Therefore, it doesn't make sense to ask for the probability of a non-integer value like 1.5.
We can use the Poisson probability mass function to calculate the probability of any integer value of X. Specifically, the probability of X = k is given by:
P(X = k) = (e^-2 * 2^k) / k!
Using this formula, we can calculate the probability of X taking on any integer value. For example:
P(X = 0) = (e^-2 * 2^0) / 0! = 0.1353
P(X = 1) = (e^-2 * 2^1) / 1! = 0.2707
P(X = 2) = (e^-2 * 2^2) / 2! = 0.2707
P(X = 3) = (e^-2 * 2^3) / 3! = 0.1805
P(X = 4) = (e^-2 * 2^4) / 4! = 0.0903
etc.
Note that the sum of all these probabilities must be equal to 1, since X is a discrete random variable that takes on one of these integer values.
Therefore, it doesn't make sense to ask for the probability of a non-integer value like 1.5.
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If the standard deviation of a Poisson variate X is 2, what is P (1.5 < X < 2.9)?a)0.231b)0.158c)0.15d)0.144Correct answer is option 'D'. Can you explain this answer?
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