1. If ‘m’ is the mean of Poisson Distribution, the P(0) is given by ___________
a) e-m
b) em
c) e
d) m-e
Explanation: P(x)=\(\frac{e^{-m}m^x}{x!}\)
Put x = 0, to obtain e-m.
2. In a Poisson distribution, the mean and standard deviation are equal.
a) True
b) False
Explanation: In a Poisson Distribution,
Mean = m
Standard Deivation = m1⁄2
∴ Mean and Standard deviation are not equal.
3. For a Poisson Distribution, if mean(m) = 1, then P(1) is?
a) 1/e
b) e
c) e/2
d) Indeterminate
Explanation: P(x)=\(\frac{e^{-m}m^x}{x!}\)
Put m = x = 1, (given) to obtain 1/e.
4. 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
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.
5. Normal Distribution is applied for ___________
a) Continuous Random Distribution
b) Discrete Random Variable
c) Irregular Random Variable
d) Uncertain Random Variable
Explanation: This is the rule on which Normal distribution is defined, no details on this as of why For more knowledge on this aspect, you can refer to any book or website which speaks on the same.
6. The shape of the Normal Curve is ___________
a) Bell Shaped
b) Flat
c) Circular
d) Spiked
Explanation: Due to the nature of the Probability Mass function, a bell shaped curve is obtained.
7. Normal Distribution is symmetric is about ___________
a) Variance
b) Mean
c) Standard deviation
d) Covariance
Explanation: Due to the very nature of p.m.f of Normal Distribution, the graph appears such that it is symmetric about its mean.
8. For a standard normal variate, the value of mean is?
a) ∞
b) 1
c) 0
d) not defined
Explanation: For a normal variate, if its mean = 0 and standard deviation = 1, then its called as Standard Normal Variate. Here, the converse is asked
9. The area under a standard normal curve is?
a) 0
b) 1
c) ∞
d) not defined
Explanation: For any probability distribution, the sum of all probabilities is 1. Area under normal curve refers to sum of all probabilities
10. The standard normal curve is symmetric about the value ___________
a) 0.5
b) 1
c) ∞
d) 0
Explanation: Normal curve is always symmetric about mean, for standard normal curve or variate mean = 0