Reg No. 02000५ 42 0405 280॥16:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

Fourth semester B.Tech examinations (S), September 2020

Course Code: MA204
Course Name: PROBABILITY, RANDOM PROCESSES AND NUMERICAL METHODS
(AE, EC)
Max. Marks: 100 Duration: 3 Hours
Normal distribution table is allowed in the examination hall.
PART A
Answer any two questions
1 2) Let ‏عط ع[‎ a random variable taking values —1,0 and 1such that P(X ಎ -1( =

2P(X = 0) = P(X = 1). Find (i) the pdf of X (ii) the mean of (2X — 5).
b) A pair of dice is thrown 5 times. If getting a doublet is considered to be a success,
use Binomial distribution to find the probability of getting (1) atleast 2 successes (ii) 8

at most 2 successes (iii) exactly 2 failures.

1௮

a) If f(x) = ६२८०९ >, x > 0, find k, mean and variance of the random variable. 7

b) The length of time (in minutes) a person speaks over the phone follows an
exponential distribution with mean 4. Find the probability that the person will talk for 8
(i) more than 8 minutes (ii) between 3 and 6 minutes (iii) less than 2 minutes.

3 8) Fita Poisson distribution 10 the following data:

b) The marks obtained by students in an intelligence test follow normal distribution
with mean 45 and standard deviation 25. Find the percentage of students who scored 8
marks (i) more than 80 (ii) between 30 and 70 (iii) below 35

PART B
Answer any two questions
4 a) A random sample of size 200 is taken from a population whose mean is 50 and

variance is 600. Using Central Limit theorem, find the probability that the mean of 7
the sample X will not differ from (८ = 50 by more than 5.
b) The joint pdf of X,Y is given by f(x,y) = k(x + 2y),x = 1,2,3; + = 1,2,3. Find

(i) k (11) marginal pdf of X,Y (iii) P(X > 3,7 2 2). ١

5 ஐ The power spectral density function of a random telegraph signal process is S(w) =
>. Find the corresponding auto correlation function and the power of the process. 1
0) {X(®)} is arandom process with mean 2 and auto correlation 8

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