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IGNOU MST 3 2024 Solution

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Last Date of Submission of IGNOU MST-03 (PGDAST) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Semester Wise
January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam).
July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).

Title Name	ignou MST 3 solved 2024
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	PG DIPLOMA PROGRAMMES
Course Code	PGDAST
Course Name	Post Graduate Diploma in Applied Statistics
Subject Code	MST 3
Subject Name	Probability Theory
Year	2024
Session	-
Language	English Medium
Assignment Code	MST-03/Assignmentt-1//2024
Product Description	Assignment of PGDAST (Post Graduate Diploma in Applied Statistics) 2024. Latest MST 03 2024 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU MST-03 (PGDAST) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam). Semester Wise January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam). July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Assignment Code	MST 3/2024

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Questions Included in this Help Book

Ques 1.

Which of the following statements are true or false? Give reason in support of your answer.

a) When two dice are thrown simultaneously then total number of sample points in the
sample space will be 12.
b) Expected value of a continuous random variable X is defined as
$E(x) = \int_{\infty }^{x}xf(x) dx$
.
c) If X and Y are independent random variable then $V(X - Y) = V(X) - V (Y)$ .
d) If $X \sim B(4,3)$ then variance of X is 12.
e) If probability density function of a normally distributed random variable X is
$f(x) = \frac{1}{6\sqrt{2\pi}}e^{\frac{1}{2}\left ( \frac{x-46}{6} \right )^2}$ , $- \infty <x<\infty$
then variance of X is 36.

Ques 2.

An insurance company selected 6000 drivers from a city at random in order to find a
relationship between age and accidents. The following table shows the results to these 6000 drivers.

Age of drivers (in years) Class Interval	Accidents in one year
	0	1	2	3	4 or more
18 – 25	700	310	225	110	85
25 – 40	1100	290	200	105	80
40 – 50	1200	235	175	80	55
50 and above	600	205	140	70	35

If a driver from the city is selected at random, find the probability of the following events:
a) Age lying between 18 – 25 and meet 3 accidents
b) Age lying between 18 – 40 and meet 1 accident
c) Age more than 25 years and meet at most one accident
d) Having no accident in the year
e) Age lying between 18 – 40 and meet at least 3 accidents

Ques 3.

Determine the constant k such that the function $f(x) = kx^2(1-x)^5, 0<x<1$ is a beta distribution of first kind. Also, find its mean and variance

Ques 4.

An insurance company insured 2000 scooter drivers, 3000 car drivers and 5000 truck
drivers. The probabilities that scooter, car and truck drivers meet an accident are 0.02, 0.04, and 0.25 respectively. One of the insured persons meets with an accident. What is the probability that he is a
a) Scooter driver
b) Car driver

Ques 5.

The following table represents the joint probability distribution of the discrete random variable

X	Y	1	2	3
1		0.2	0.2	0.1
2		0.1	0.3	0.1

Find

a) The marginal distributions.

b) The conditional distribution of Y given X = 2

Ques 6.

A rain coat dealer can earn Rs 800 per day during a rainy day. If it is a dry day, he can lose Rs 150 per day. What is his expectation, if the probability of rain is 0.6?

Ques 7.

A player tosses two unbiased coins. He wins Rs. 10 if 2 heads appear, Rs. 5 if one head appears and Rs 1 if no head appears. Find the expected value of the amount won by him

Ques 8.

Let X and Y be two independent random variables such that $X \sim B(5, 0.06)$ and $Y \sim B(4, 0.6)$ . Find $P[X+Y>1]$

Ques 9.

Comment on the statement: “The mean of a binomial distribution is 4 and variance 5”.

Ques 10.

If the probability that an individual suffers a bad reaction from an injection of a given
serum is 0.002, determine the probability that out of 400 individuals
(i) exactly 2
(ii) more than 3
(iii) at least one
individuals suffer from bad reaction.

Ques 11.

A die is rolled. If the outcome is a number greater than 2, what is the probability that it is an odd prime number?

Ques 12.

A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit 2 out of 5 shots. Find the probability that the target being hit when they both try.

Ques 13.

Events A, B, C are mutually exclusive and exhaustive. If odds against A are 4:1 and against B are 3: 2 . Find the odds against event C.

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