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SECTION-A
1. Answer the following questions. [lx 10]
(a) Let Aand Bbe two mutually exclusive events such that
AUB= S and P(A)=3P(B) then find P(B).
(b) Let A
and B be two events with probabilities P(A) = 0.5,
P(B) = 0.375 and P(AnB) = 0.25 then find P(A'n B).
(c) If the distribution functionF(*)of a continuous random
variable Xis given as:
(k(*-1)»for 1<xs3
F) = 0 for xs1
1 for x> 3
Find the value of kand find the pdf f).
(d) If the mean and variance of a random variable X are 0.5
and 3 respectively then find the mean and variance of the
random variable Y = 3X + 2.
(e) LetX be the time between two successive arrivals at the
drive-up window of a local bank. X has an exponential
distribution with =2. Find the expected time between two
successive arrivals at the drive-up window.
KIlIT-DU 2024 SOTAMumn End Semester Examination-2024
() Show that Ioa'=E(X') -p where and Garc mean and
variance of the random variablc Xrespcctively.
(0) Lethe random variable Xhas an exponential
distribution
with variance 1, then find the 50" percentile of X
(h) If the random variable X follows a Poisson distribution
such that P(X = 1) = P(X = 2). ind mean and P(X = 0)
() If A, B are independent with P(A) = 0.3 and P(A u
B) = 0.8, then find P(B).
(i) Find the sa1ple mean and sample variance for the data
2,7.3,4,5,6
SECTION-B
2. (a) Define Poisson distribution and then find the mean and
variance of Poisson distribution.
(b) Define conditional probability for any two events Aand
B. A computer consulting fim presently has bids out
on three projects. Let A; =(awarded project i}, for i
=1, 2, 3, and suppose that P(A) = 0.22, P(A;) =
0.25, P(A;) = 0.28, P(A,n Az) = 0.11, P(A, n
A;) = 0.05, P(A, NAz) = 0.07, P(A, n A, n A_) =
0.01. Compute the probability of the following events:
a) P(A,|A
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Total Pages: 4 Current Page: 2
SECTION-A
1. Answer the following questions. [lx 10]
(a) Let Aand Bbe two mutually exclusive events such that
AUB= S and P(A)=3P(B) then find P(B).
(b) Let A
and B be two events with probabilities P(A) = 0.5,
P(B) = 0.375 and P(AnB) = 0.25 then find P(A'n B).
(c) If the distribution functionF(*)of a continuous random
variable Xis given as:
(k(*-1)»for 1<xs3
F) = 0 for xs1
1 for x> 3
Find the value of kand find the pdf f).
(d) If the mean and variance of a random variable X are 0.5
and 3 respectively then find the mean and variance of the
random variable Y = 3X + 2.
(e) LetX be the time between two successive arrivals at the
drive-up window of a local bank. X has an exponential
distribution with =2. Find the expected time between two
successive arrivals at the drive-up window.
KIlIT-DU 2024 SOTAMumn End Semester Examination-2024
() Show that Ioa'=E(X') -p where and Garc mean and
variance of the random variablc Xrespcctively.
(0) Lethe random variable Xhas an exponential
distribution
with variance 1, then find the 50" percentile of X
(h) If the random variable X follows a Poisson distribution
such that P(X = 1) = P(X = 2). ind mean and P(X = 0)
() If A, B are independent with P(A) = 0.3 and P(A u
B) = 0.8, then find P(B).
(i) Find the sa1ple mean and sample variance for the data
2,7.3,4,5,6
SECTION-B
2. (a) Define Poisson distribution and then find the mean and
variance of Poisson distribution.
(b) Define conditional probability for any two events Aand
B. A computer consulting fim presently has bids out
on three projects. Let A; =(awarded project i}, for i
=1, 2, 3, and suppose that P(A) = 0.22, P(A;) =
0.25, P(A;) = 0.28, P(A,n Az) = 0.11, P(A, n
A;) = 0.05, P(A, NAz) = 0.07, P(A, n A, n A_) =
0.01. Compute the probability of the following events:
a) P(A,|A
