I Year Sem- II Model Paper
Model Paper- I
SUBJECT: STATISTICS
Paper-II: Probability
Distributions
SECTION - A
Write any
Five questions
5 X 4 = 20
1. Define
Bernoulli distribution. Obtain mean and variance.
2. Derive mode of Binomial
distribution.
3. Derive m.g.f of Poisson
distribution. Hence find mean and variance.
4. State and Prove Additive
property of Geometric distribution.
5. Obtain median of Normal
distribution.
6. Define Cauchy Distribution
and Write its properties.
7. Derive m.g.f of Uniform
Distribution.
8. Explain weak law of large
numbers.
SECTION - B
Answer all 4 Questions: 4 X 15 = 60
9.(a).(i). Derive
Recurrence relation for the moments of Poisson distribution.
(ii). It is
stated 2% of razor blades supplied by a company are defective.A random sample of 200 blades is drawn from a
lot. Find the probability of 3 or more are defectives. (OR)
(b). Define Hyper
geometric distribution. Obtain mean and variance.
10.(a). Derive m.g.f of Geometric distribution. State and
prove its Lack of memory property. (OR)
(b). State and
prove additive property of Negative binomial distribution. And show that
Poisson distribution is a limiting case of the Negative binomial distribution.
11.(a). Calculate Even and Odd moments of Normal
distribution.
(OR)
(b). Calculate
mean and variance of Beta Distribution of 1st kind and 2nd
kind.
12.(a). Obtain m.g.f and c.g.f of Exponential distribution.
Also Find b1 & b2.
(OR)
(b). Obtain m.g.f
of Gamma distribution and show that Gamma distribution tends to Normal
distribution as l ® ¥.
Model Paper II
SECTION- A
I.
Answer any Five questions: 5*4=20M
1. Define
Bernoulli distribution. Obtain Mean and
Variance.
2. Define
discrete uniform distribution. Obtain Mean and Variance.
3. State
and prove additive property of Binomial distribution.
4. Define
Geometric distribution. Derive its moment generating function .
5. Define
Cauchy distribution, write its properties.
6. Write
chief characteristics of normal distribution.
7. The
mean and variance of a continuous uniform random variable ‘x’ are 1.5 and 0.75
respectively. Obtain the probability density function of ‘x’.
8. Sate
weak law of large numbers.
SECTION -B
II. Answer all questions: 4*15=60M
9(a).
Define negative binomial distribution. Derive its mean and variance
through expectation. (OR)
(b). Define Hyper geometric distribution,
give an example. Obtain its Mean and
Variance.
10(a).(i).
Define Binomial distribution. Obtain moment generating function.
(ii). Prove that Binomial
distribution is the limiting case of Hyper geometric
distribution by stating the
conditions.
(OR)
(b).(i). Show that Poisson distribution
satisfies the reproductive property.
(ii).The number of monthly breakdowns
of the computer is a random variable “X” having a Poisson Distribution with mean 2. Find the probability that this computer will function
for a month
(a).Without a breakdown (b).With exactly one breakdown.
11(a).
Define Standard normal distribution. Derive normal distribution is the limiting case of Poisson distribution. (OR)
(b). (i) Define exponential distribution.
Obtain its m.g.f.
(ii) State and prove its lack of memory
property.
12(a).
Show that for a Normal distribution, QD :
MD : SD =
10 :
12 : 15
(OR)
(b) Define Beta
distribution of 1st and 2nd kinds.
Obtain Mean and Variance of these
distributions.
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