Reg No.: Name:

E4802
Total Pages: 2

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FOURTH SEMESTER B.TECH DEGREE EXAMINATION, APRIL 2018

Course Code: MA204

Course Name: PROBABILITY, RANDOM PROCESSES AND NUMERICAL METHODS

Max. Marks: 100

1 a)
b)
2 a)
b)
3 a)
b)
4 a)
b)

(AE, EC)

(Normal distribution table is allowed in the examination hall)
PARTA
Answer any two full questions, each carries 15 marks
A random variable X has the following probability distribution:

_ त

Find: i) The value of k ii) Evaluate P(X ಆ 2) and P(—2 > ೫ < 2)
111) Evaluate the mean of X
The probability that a component is acceptable is 0.93. Ten components are picked
at random. What is the probability that:
i) At least nine are acceptable 1) At most three are acceptable.
Suppose that the length of a phone call in minutes is an exponential random variable

⋅ 1 ⋅⋅ ⋅ ⋅
with parameter 4 = a If someone arrives immediately ahead of you at a public

telephone booth, find the probability that you will have to wait:

i) More than 10 minutes ii) Between 10 and 20 minutes.
For a normally distributed population, 7% of items have their values less than 35
and 89% have their values less than 63. Find the mean and standard deviation of the
distribution.
Fit a binomial distribution to the following data and calculate the theoretical
frequencies.

(8 |
f 2 17 13 15 | 25 16 11 |8 | 3

The time between breakdowns of a particular machine follows an exponential
distribution, with a mean of 17 days. Calculate the probability that a machine breaks
down in a 15 day period.

PART B
Answer any two full questions, each carries 15 marks
The joint PDF of two continuous random variables X and Y is given by

_ (100 010೬2೫) = { 0 otherwise '
Find: i)k ii) The marginal distributions of X and Y

iii) Check whether X and y are independent.
A distribution with unknown mean u has variance equal to 1.5. Use Central Limit
Theorem to find how large a sample should be taken from the distribution in order
that the probability will be at least 0.95 that the sample mean will be within 0.5 of
the population mean.

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Duration: 3 Hours

Marks

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