1. Poisson distribution is a limiting case of ___________________.
a) Negative Binomial b)Geometric c)Hypergeometric
Ans: a
2. Suppose $X$ follows Negative Binomial distribution with the parameters (r,p). Then what will be the distribution of X when $r=1$?
a) Negative Binomial b)Geometric c)Hypergeometric
Ans: b
3."Geometric distribution follows lack of memory property" is it true or false?
a)True b)False
Ans: a
4) $P(X=x)= q^xp; x=0,1,2,........; p\leqslant 1, q=1-p$. then var of the $X$ is ____________.
a)$\frac{q}{p^2}$ b)$\frac{p}{q^2}$ c) $\frac{p+1}{q^2}$
5. Suppose $X$ and $Y$ have geometric distribution. The the distribution of $X$ given $X+Y$ is
a) Uniform b) Negative Binomial c) Binomial
Ans:a
MCQs on Poisson Distribution
6.For Geometric distribution
a) mean>var b) var>mean c) mean=var
7.Suppose $X$ follows Hypergeometric distribution with the parameters $n,k,.M,N$; $k=0,1,2,....,min(n,M)$. then the mean of the distribution is
a)$\frac{nM}{N}$ b)$\frac{kM}{N}$ c)$\frac{nM}{k}$
8. Suppose $X$ follows Hypergeometric distribution with the parameters $n,k,.M,N$;Then X will follow Binomial if
a)$N\rightarrow \infty$, $\frac{M}{N}\rightarrow p$ b)$M\rightarrow \infty$, $\frac{M}{N}\rightarrow p$ c)$N\rightarrow \infty$, $\frac{N}{M}\rightarrow p$
Ans: a
9.Pgf of Geometric distribution with parameter $p$; $x=0,1,2......$ is
a)$\frac{p}{1-qs}$ b) $\frac{q}{1-ps}$ c) $\frac{p}{1-ps}$
10. The pgf of Nergative Binomial distribution is with parameter $r,p$.$x=0,1,2......$
a)$[\frac{p}{1-qs}]^r$ b) $[\frac{q}{1-ps}]^r$ c) $[\frac{q}{1-qs}]^r$