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Reg No.:_ Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION(S), DECEMBER 2019

Course Code: MA204
Course Name: PROBABILITY, RANDOM PROCESSES AND NUMERICAL METHODS

Max. Marks: 100 Duration: 3 Hours
Normal distribution table is allowed in the examination hall.
PARTA

Answer any two full questions, each carries 15 marks

1 a) A coin is biased so that the head is twice as likely to appear as the tail. The coin is tossed (7)
twice. Find the expected value of the number of heads. Also find the variance of number
of heads.
b) Show that Poisson distribution is the limiting case of Binomial distribution as (8)

7 -> ०0, -> 0.

2 3 The time required to repair a machine is exponentially distributed with parameter त What (ಗ)
is the probability that (i) repair time exceeds 2 hrs (ii) repair time is between 3 hrs and 5
hrs?

b) A random variable X has the following probability density function: (8)
f(x) =kx(2-x),0 distribution function.

3 9) Fit a Poisson distribution to the following data: (7)

b) In an intelligence test administrated on 1000 children, the average was 60 and the standard (8)
deviation was 20. Assuming that the marks obtained by the children follow a normal
distribution, find the number of children who have scored (i) above 90 marks (ii) below 40
marks (iii) between 50 and 80 marks

PART छ
Answer any two full questions, each carries 15 marks

4 a) Let ¥,¥ ,......,¥ 75 are independently and identically distributed random variables (7)

following Poisson distribution with parameter A = 2. Use Central Limit Theorem to

estimate P(120 ಇ 5.5 > 160), where $7, =X, + ഇ...

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