Reg No.:

B4A0002
Total Pages: 2

Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, JULY 2017
Course Code: MA202

Course Name: PROBABILITY DISTRIBUTIONS, TRANSFORMS AND NUMERICAL

METHODS

Max. Marks: 100 Duration: 3 Hours

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Normal distribution table is allowed in the examination hall.
PART A (MODULES I AND II)
Answer two full questions.

A random variable X has the following probability mass function (8)
XxX: 0 1 2 3 4 5 6 7

P(x): 0 1 2k 21 310 12 शत 7k? +k

Find (i) value of k (1) 00 ೩% ೪೩5) (iii) P(x >6)

An insurance company agent accepts policies of 5 men, all of identical age and good (7)
health. Probability that a man of this age will be alive 30 years is 2 . ह the

probability that in 30 years (i) all5 men (10) at least one men will be alive.
Show that for a poisson distribution with parameter 2, mean = variance = ۸ (7)

In a given city 6% of all drivers get at least one parking ticket per year. Use the (8)
poisson approximation to the binomial distribution to determine the probabilities

that among 80 drivers (randomly chosen in this city)

(i) 4 will get at least one parking ticket in any given year

(ii) at least 3 will get at least one parking ticket in any given year

(iii) anywhere from 3 to 6 inclusive, will get at least one parking ticket in any given

year.

The marks obtained in mathematics by 1000 students are normally distributed with (6)
mean 78% and standard deviation 11%. Determine

(1) How many students got marks above 90%

(ii) What was the highest mark obtained by the lowest 10% of students

Derive the mean and variance of the uniform distribution in the interval (a,b) (7)

PART B (MODULES III AND IV)
Answer two full questions.

Express f(x) = 1,0 0. ೫೨7, 1
a Fourier sine integral and evaluate 1 ೮೦5೫ sinxw dw
@
Using Fourier integral representation show that (8)
| sinxwdw = "x, if00 ५2 2
* if x=1
4
0, ifx>1

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