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Student Declaration

I__________________________________ Registration No.__________________, hereby

declare that by attempting the paper for the course _________________________________,

I will not be involved in any kind of cheating/copying/plagiarizing in solving the short

questions based paper of Final Term Examination Spring 2021. I take full responsibility of

my conduct. If I found involved in any kind of such activity of cheating/copying/plagiarizing,

then Institute reserves the right to take any disciplinary action against me.

Student Signature
Final Exam / Spring 2021 (Paper Duration 24 hours)
(Online Assignment Based Question Paper)

Course No.: STT – 500 Course Title: Statistics and Probability


Total Marks: 30 Date of Exams: 07-07-2021
Degree: BSCS/ IT Semester: 2nd Section: A& B
Marks
Q.No. 1 2 3 4 5 6 7 8 9 10 Obtained/
Total Marks
Marks
Obtaine
d
Obtained Marks in Words:
Name of the Teacher:
Who taught the course: Signature of Teacher / Examiner:

To be filled by Student

Registration No.: Name:

(THEORETICAL/PRACTICAL EXAMINATION)

Answer the following questions


Q.No.1. Write the answer to the following question. (Marks 2 x 5 = 10)
(i) Difference between the binomial and hyperdeometric distribution in discrete probability.
Answer: _______ ______

(ii) A coin and a dice is rolled, find the sample space of these two events.

Answer: _______ ______

(iii) A box contains 15 items, 4 of which are defective. Four items are selected. What is the

probability that the first item is good, 2nd is defective, 3rd is good and 4th is defective.
Answer: _______ ______
(iv) What is the difference between mutually and not mutually exclusive events with
example?
Answer: _______ ______

(v) A wished hand contains exactly two red cards.

Answer: _______ ______

Q.No.2.(a) Assuming that the weekly demand for the video recorded is a poisson
distribution with variance 3, find the probability that the shop sells (i) at least 3 in a week
(ii) at most 7 in a week (iii) more than 20 in a month (4 week) (Marks 03)
Answer: _______ ______

(b) A Surgeon probability of a successful operation is 0. 2 for each operation, and that the 6
operations are independent, compute the probability that, in order to operate: (Marks 03)
(i) It takes more than two operations.

(ii) The number of operations required is between four and six (inclusive).

(iii) Find its mean and variance to the following distribution.

Answer: _______ ______

(c) Find the value of K so that the function f (x) defined as follow, may be density function.
Also determine its mean and standard deviation. (Marks 04)
f(x) = k x 3 ( 1 – x ) 0 < x < 1
= 0 otherwise

Answer: _______ ______


Q.No.3.(a) State and prove that two events A and B will both occur is equal to the
probability that one of the events will occur multiplied by the conditional probability that
the other event will occur given that the first event has occurred. (Marks 02)

Answer: _______ ______

(b) A deck of playing cards contains 20 cards: 14 black and cards 6 red cards. 5 cards are
drawn randomly without replacement. What is the probability that exactly 4 red cards are
drawn? The probability of choosing exactly 4 red cards is. Also calculate the mean and
variance. (Marks 03)
Answer: _______ ______

(c) A random variable x is a binomial distribution with mean 4 and variance 3 compute

P (X = 4) and P (X = 2) (Marks 02)


Answer: _______ ______

(d) A dell laptop company made by consists of two types of laptop, gray color laptop and
black color laptop. In the process of manufacturing of gray color laptop, 98 out of 150 are
non defective. And in the manufacturing process of black color laptop, 95 out of 150 are non
defective. Calculate the probability that the assembled type is non defective. (Marks 03)
Answer: _______ ______

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