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# IGNOU MST 003 Probability Theory 2019

IGNOU MST 003 Probability Theory 2019

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• IGNOU MST 003 Probability Theory

• IGNOU PGDAST (Post Graduate Diploma in Applied Statistics) Solved Assignment 2019

• Latest 2019 Solved Assignment

MST 003 Probability Theory

• PGDAST (DIPLOMA PROGRAMMES) MST 003

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### Questions :

1. If A and B are any two events defined on a sample space S then P(A ∪B) = P(S)  always holds.

2. Cumulative distribution function of a discrete random variable is always strictly increasing.

3. If X is a discrete random variable with probability mass function (pmf)

 X 0 1 2 3 P[X = x ] $\frac{1}{8}$ $\frac{1}{4}$ $\frac{1}{2}$ a

then value of a will be 1.

4. If X and Y are two independent random variables then P[X ≥ 2|Y > 1] < P[X ≥ 2].

5. Suppose that you spin the dial shown in the figure so that it comes to rest at a random position.

The probability that the dial will land somewhere between 0 and 45 will be 1/4.

6. First check whether the following function is a valid density function? If it is a valid density then obtain its cumulative probability function F(x). If it is a valid density then finally calculate P(7 ≤ X ≤ 8) either using f(x) or F(x).

$f(x)= \left\{\begin{matrix} \frac{2}{25}(x-5), &5\leq X\leq 10 & \\ & &ifx< 0 \\ 0,&otherwise & \end{matrix}\right.$

7. The joint density function of random variables X and Y is given by

$f(x,y)=\left\{\begin{matrix} 14e^{-2x-7y} ,&x\geq 0,y\geq 0 \\ 0,&otherwise \end{matrix}\right.$

Are X and Y independent?

8. A particular game is played where the contestant spins a wheel that can land on the number 1, 5, 30 with probabilities of 0.50, 0.45 and 0.05, respectively. The contestant pays INR5 to play the game and is awarded the amount of money indicated by the number where the spinner lands. Is this a fair game? [By fair, it is meant that the contestant should have an expected return equal to the price she pays to play the game.]

9. Suppose two fair dice are tossed where each of the 36 possible outcomes is equally likely to occur. Knowing that the first die shows a 4, what is the probability that the sum of the two dice equals at least 7.

10. Suppose that there are m students in a room. What is the probability that at least two of them have the same birthday? Assume that every day of the year is equally likely to be a birthday, and disregard leap years. That is, assume there are always 365 days to a year. [Hint: Attack the problem by first calculating probability of complement event and then use P(E) = 1 – P( $\overline{E}$)]

11. The A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is the probability that

(i) 3 of them are Ambassadors and 2 are Fiats,

(ii) at least 3 of them are Ambassadors, and

(iii) all 5 are of the same make?

12. The probability that a player hits a target is 0.24. He fires 6 times. What is the probability of hitting the target exactly twice?

13. What is the probability that 5th success is obtained in 9th trail if probability of success and failure do not vary from trial to trail.

14. Metro trains in a certain city run every 9 minutes between 6.15 a.m. to 11.15 p.m. What is the probability that a commuter entering the station at a random time during this period will have to wait at least five minutes?

15. Obtain mean and variance for the beta distribution whose density is given by

$f(x)=\frac{280x^{3}}{(1+x)^{9}},\: \: 0< x< \infty$

16. A car manufacturer purchases car batteries from two different suppliers A and B. Suppose supplier A provides 60% of the batteries and supplier B provides the rest. If 6% of all batteries from supplier A are defective and 4% of the batteries from supplier B are defective. Determine the probability that a randomly selected battery is not defective.

17. An item is produced by a machine in large numbers. The machine is known to produce 5% defectives. A quality control engineer is testing the items randomly. What is the probability that at least 5 items are examined in order to get 2 defectives?

*This Assignment/Project Help Book is only for demonstration Purpose that how to solved/write them. As IGNOU is a distance Learning Approach, many students were not aware how to write and how much to write the Assignment/Project. So, it is our request treat it as a help book guide. First read the entire .pdf file after buying and then write yourself in your own words.

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## Details

### MST 003 is a subject of Probability Theory

• IGNOU MST 003 Probability Theory

• IGNOU PGDAST (Post Graduate Diploma in Applied Statistics) Solved Assignment 2019

### • Latest 2019 Solved Assignment

MST 003 Probability Theory

• PGDAST (DIPLOMA PROGRAMMES) MST 003

• Buy Now MST 003 Solved Assignment

TUTOR MARKED ASSIGNMENT
MST-003: Probability Theory
Course Code: MST-003
Assignment Code: MST-003/TMA/ 2019

This assignment is to be submitted at the Study Centre. You cannot fill the Exam Form for this course till you have submitted this assignment. So solve it and submit it to your study centre at the earliest. If you wish to appear in the TEE, June 2019, you should submit your TMAs by March 31, 2019. Similarly, If you wish to appear in the TEE, December 2019, you should submit your TMAs by September 30, 2019.

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UNIVERSITY IGNOU PG DIPLOMA PROGRAMMES PGDAST Post Graduate Diploma in Applied Statistics MST 003 Probability Theory SOFT COPY 2019 Assignment
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