Reg No. 02000M A20205200ame:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

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

Course Code: MA202
Course Name: PROBABILITY DISTRIBUTIONS, TRANSFORMS AND NUMERICAL
METHODS
Max. Marks: 100 Duration: 3 Hours

Normal distribution table is allowed in the examination hall.
PART A (MODULES I AND 11)
Answer two full questions.

1 a) Let Xbe 8 discrete random variable with mean 10 and variance 25. Find the positive 7
values of a and / such that Y = aX — B has mean 0 and variance 1.

b) Derive the mean and variance of a Poisson Distribution. 8

2 a) Ifacontinuous random variable has the probability distribution function 7

ke~** ifx > 0

109 = (0 if x > 0
then find (i) value of k (ii) P[O > X > 2] (iii) P[X > 1.5]
b) Ina Normal Distribution, if 6% of the items are below 60 and 39% are above 70, 8
then find the mean and standard deviation.
3 a) Out of 2000 families with 4 children each, how many would you expect to have (i) 7
at least one boy (ii) at most one boy

b) If X follows a uniform distribution in (—2,2), then (i) find P[|X — 1| > 2] (11) find 8
k for which P[X > k] = 3 (iii) Distribution function

PART B (MODULES 111 AND IV)
Answer two full questions.
sinx 1/2 0 > 2 > 7 7

Find the Fourier Sine Integral of f(x) = { 0 if x>n

b) Find the Fourier Cosine Transform of f(x) = e~**. Hence deduce that 8

ர்‌ 005 22 7 €-8
0 x24+16 ˆ“ 8
3 2) Using Convolution theorem, evaluate the Inverse Laplace Transform of ന്ന 7
b) E ⋅ ∙≳ ⋅⋅ −∣ = 5+5 | 8
valuate (i) L[t sin?2¢] (ii) ^ । [द्र

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