1. The 4th order central moment of poisson distribution is -
a) $\small 2\lambda^{2} + \lambda$
b) $\small 3\lambda^{2} + \lambda$
c) $\lambda$
d) None
2.
A car hire firm has two cars which it fires out day by day. The number
of demands for a car on each day is distributed as Poisson variate with
mean 1.5. Calculate the proportion of days on which neither car is used.
a) 0.256 b) 0.2231 c) 0.2561 d) 0.3211
Ans. b) 0.2231
3.If $X$ and $Y$ follow Poisson distribution, then what will be distribution of $X$ given $X+Y$?
a)Poisson b) Binomial c)Normal d) none of them
Ans: b
4.If $X$ follows Poisson distribution with Parameter $\lambda$, then what will be the $p(x+1)$ at $x=0$ ?
a)$\frac{\lambda}{x+1}p(0)$ b)\frac{\lambda}{\lambda+1}p(0) c)\frac{x}{x+1}p(0) d)\frac{\lambda}{\lambda+1}p(0)
Ans: a
5. $P(X=2)=9P(X=4)+90P(X=6)$ , Here X follows Poisson distribution. Find $\lambda$ ?
a)1b)2c)3d)4
Ans: a
6.If $X$ and $Y$ follows Poisson distribution individually then what will be the var of $X-2Y$, when $P(X=1)=P(X=2)$ and P(Y=2)=P(Y=3)$.
a)28 b)14 c)25 d)35
Ans: b
7.In a Poisson frequency distribution frequency corresponding to 3 successes is 2/3 times frequency corresponding to 4 successes. Find the mean.
a)12 b)6 c)7 d)9
Ans: b
8. For Poisson distribution $\lambda$ is always
a) Positive b) Negative c) Positive or Negative d) None of it
Ans: b
4.
A manufacturer of cotter pins knows that 5% of his product is
defective. If he sells cotter pins in boxes of 100 and guarantees that
not more than 10 pins will be defective, what is the approximate
probability that a box will fail to meet the guaranteed quality?
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5.
Six coins are tossed 6,400 times. Using the Poisson distribution, find
the approximate probability of getting six heads r times.
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6.
In a book of 520 pages, 390 typo-graphical errors occur. Assuming
Poisson law for the number of errors per page, find the probability that
a random sample of 5 pages will contain no error.
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7.
If $\small X_i(i=1,2,..,n)$ are independent Poisson variates with
parameters $\small \lambda_i; i= 1,2,...,n$ respectively, then $\small
\sum_{i=1}^{n} X_i$ is follows what ?
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