Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > If X is a Poisson variate with P(X = 0) = 0.6...
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If X is a Poisson variate with P(X = 0) = 0.6, then the variance of X is:
- a)In (1/5)
- b)log1015
- c)0
- d)ln 15
Correct answer is option 'A'. Can you explain this answer?
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If X is a Poisson variate with P(X = 0) = 0.6, then the variance of X ...
Calculating the Variance of a Poisson Variate:
To calculate the variance of a Poisson variate, we use the formula Var(X) = λ, where λ is the mean of the Poisson distribution. In this case, we are given P(X = 0) = 0.6, which implies that the mean of the distribution is λ = 0.6.
Calculating the Variance:
Given that the mean of the Poisson distribution is λ = 0.6, we can calculate the variance using the formula Var(X) = λ. Therefore, Var(X) = 0.6.
Comparing with the Options:
a) In (1/5): Var(X) = 0.6 = 6/10 = 3/5. This option is not correct.
b) log1015: This option is not related to the calculation of the variance of a Poisson variate.
c) 0: The variance of X is not equal to 0, as we calculated Var(X) = 0.6.
d) ln 15: This option is not relevant to the calculation of the variance of a Poisson variate.
Conclusion:
The correct answer is option 'A' - In (1/5), as we have calculated Var(X) = 0.6, which can also be expressed as 6/10 or 3/5. Therefore, the variance of X is indeed in the form of 1/5.
To calculate the variance of a Poisson variate, we use the formula Var(X) = λ, where λ is the mean of the Poisson distribution. In this case, we are given P(X = 0) = 0.6, which implies that the mean of the distribution is λ = 0.6.
Calculating the Variance:
Given that the mean of the Poisson distribution is λ = 0.6, we can calculate the variance using the formula Var(X) = λ. Therefore, Var(X) = 0.6.
Comparing with the Options:
a) In (1/5): Var(X) = 0.6 = 6/10 = 3/5. This option is not correct.
b) log1015: This option is not related to the calculation of the variance of a Poisson variate.
c) 0: The variance of X is not equal to 0, as we calculated Var(X) = 0.6.
d) ln 15: This option is not relevant to the calculation of the variance of a Poisson variate.
Conclusion:
The correct answer is option 'A' - In (1/5), as we have calculated Var(X) = 0.6, which can also be expressed as 6/10 or 3/5. Therefore, the variance of X is indeed in the form of 1/5.
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Community Answer
If X is a Poisson variate with P(X = 0) = 0.6, then the variance of X ...
Given
In Poisson distribution
P(X = 0) = 0.6
Formula
Poisson distribution is given by
f(x) = e-λλx/x!
Calculation
P(X = 0) = e-λλ0/0!
⇒ 0.6 = e-λ
⇒ 1/eλ = 6/10 = 3/5
⇒ eλ = 5/3
Taking log on both side
⇒ logeeλ = loge(5/3)
∴ λ = Loge(5/3)
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