This set of Probability and Statistics Multiple Choice Questions & Answers (MCQs) focuses on “Poisson Distribution”.
1. In a Poisson Distribution, if ānā is the number of trials and āpā is the probability of success, then the mean value is given by?
a) m = np
b) m = (np)2
c) m = np(1-p)
d) m = p
View Answer
Explanation: For a discrete probability function, the mean value or the expected value is given by
Mean(μ)=\(\sum_{x=0}^n xp(x)\)
For Poisson Distribution P(x)=\(\frac{e^{-m}m^x}{x!}\) substitute in above equation and solve to get Āµ = m = np.
2. If āmā is the mean of a Poisson Distribution, then variance is given by ___________
a) m2
b) m1⁄2
c) m
d) m⁄2
View Answer
Explanation: For a discrete probability function, the variance is given by
Variance (v) = \(\sum_{x=0}^n x^2p(x)-\mu^2\)
Where Āµ is the mean, substitute P(x)=\(\frac{e^{-m}m^x}{x!}\), in the above equation and put Āµ = m to obtain
V = m.
3. The p.d.f of Poisson Distribution is given by ___________
a) \(\frac{e^{-m}m^x}{x!}\)
b) \(\frac{e^{-m}x!}{m^x}\)
c) \(\frac{x!}{m^xe^{-m}}\)
d) \(\frac{e^m m^x}{x!}\)
View Answer
Explanation: This is a standard formula for Poisson Distribution, it needs no explanation.
Even though if you are interested to know the derivation in detail, you can refer to any of the books or source on internet that speaks of this matter.
4. If āmā is the mean of a Poisson Distribution, the standard deviation is given by ___________
a) \(\sqrt{m}\)
b) m2
c) m
d) m⁄2
View Answer
Explanation: The variance of a Poisson distribution with mean āmā is given by V = m, hence
Standard Deviation = \(\sqrt{variance} = \sqrt{m}\)
5. In a Poisson Distribution, the mean and variance are equal.
a) True
b) False
View Answer
Explanation: Mean = m
Variance = m
ā“ Mean = Variance.
6. In a Poisson Distribution, if mean (m) = e, then P(x) is given by ___________
a) \(\frac{e^{(x-m)}}{x!}\)
b) \(\frac{e^{(m-x)}}{x!}\)
c) \(\frac{x!}{e^{(m-x)}}\)
d) \(\frac{x!}{e^{(x-m)}}\)
View Answer
Explanation: P(x)=\(\frac{e^{-m}m^x}{x!}\)
Put m = e, and get correct solution.
7. Poisson distribution is applied for ___________
a) Continuous Random Variable
b) Discrete Random Variable
c) Irregular Random Variable
d) Uncertain Random Variable
View Answer
Explanation: Poisson Distribution along with Binomial Distribution is applied for Discrete Random variable. Speaking more precisely, Poisson Distribution is an extension of Binomial Distribution for larger values ānā. Since Binomial Distribution is of discrete nature, so is its extension Poisson Distribution.
8. If āmā is the mean of Poisson Distribution, the P(0) is given by ___________
a) e-m
b) em
c) e
d) m-e
View Answer
Explanation: P(x)=\(\frac{e^{-m}m^x}{x!}\)
Put x = 0, to obtain e-m.
9. In a Poisson distribution, the mean and standard deviation are equal.
a) True
b) False
View Answer
Explanation: In a Poisson Distribution,
Mean = m
Standard Deivation = m1⁄2
ā“ Mean and Standard deviation are not equal.
10. For a Poisson Distribution, if mean(m) = 1, then P(1) is?
a) 1/e
b) e
c) e/2
d) Indeterminate
View Answer
Explanation: P(x)=\(\frac{e^{-m}m^x}{x!}\)
Put m = x = 1, (given) to obtain 1/e.
11. The recurrence relation between P(x) and P(x +1) in a Poisson distribution is given by ___________
a) P(x+1) – m P(x) = 0
b) m P(x+1) – P(x) = 0
c) (x+1) P(x+1) – m P(x) = 0
d) (x+1) P(x) – x P(x+1) = 0
View Answer
Explanation: P(x)=\(\frac{e^{-m}m^x}{x!}\)
p(x+1) = e-1 mx+1 /(x + 1)!
Divide P(x+1) by P(x) and rearrange to obtain (x+1) P(x+1) – m P(x) = 0.
Sanfoundry Global Education & Learning Series ā Probability and Statistics.
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