IGNOU MST003 Solved Assignment 2022
 AUTHOR: Narendra Kr. Sharma
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IGNOU MST003 Solved Assignment 2022
MST003 Solved Assignment is an ebook for students who want to specialise in statistics. This completed assignment will allow them to assess their degree of preparation and will be extremely beneficial. All questions and concerns have been addressed and clarified. As a result, students will comprehend the concepts of any question in the assignment.
Assignment Paper 
IGNOU MST003 Solved Assignment 2022 
Subject Name 
Probability Theory 
No.of Pages in Solution 
23 
Course 
PGDAST 
Language 
ENGLISH 
Session 
2022 
Last Date for Submission of Assignment 
For June Examination 31st March 2022 or as per dates given in the Ignou website For December Examination 30th September 2022 or as per dates given in the Ignou website 
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IGNOU MST003 Sample Solution 2022
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IGNOU MST003 Solved Assignment 2022
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IGNOU MST003 Assignment Question Paper 2022
(Probability Theory)
Note: All questions are compulsory. Answer in your own words.
1. State whether the following statements are True or False and also give the reason in support of your answer. (a) Sample space of a (i) random experiment tossing two coins simultaneously and (ii) One coin two times is the same. (b) Standard deviation of a random variable X may take any real value, i.e. its value lies in the interval \( \left(\infty \:,\infty \:\right) \). (d) If S is sample space of a random experiment and E is an event defined on this sample space then P(SE) = 1. (e) If X is a random variable having range set {0, 1, 2, 3} then the set \( \left\{x\in S:X\left(x\right)=0\right\} \) is an event having at least one outcome of the random experiment. 2. There are 4 black, 3 blue and 8 red balls in an urn. Three balls are selected one by one without replacement. What is the probability that: (i) First ball drawn is black, second one is red and third one is blue (ii) All the three balls are of the same colour 3. A random 5card poker hand is dealt from a standard deck of cards. Find the probability (in terms of binomial coefficients) of getting a flush (all 5 cards being of the same suit: do not count a royal flush, which is a flush with an ace, king, queen, jack and 10). 4. Show that \( f\left(x\right)=\left(\frac{1}{2}\right)^{x+1} \) , x = 0, 1, 2, 3, 4, 5, is a valid PMF for a discrete random variable. Also find out its CDF. 5. A group of 100 people are comparing their birthdays (as usual, assume their birthdays are independent and not on February 29, etc.). Find the expected number of pairs of people with the same birthday, and the expected number of days in the year on which at least two of these people were born. 6. Random variable X follows Beta distribution with parameters a = 3, b = 2 and has pdf \( f\left(\:x\right)\:=\begin{Bmatrix}12x^2\left(\:1x\right)\::0\:<x\:<1\\ 0;\:otherwise\end{Bmatrix} \) Find (i) CDF of X (ii) P[0<X<1/2] (iii) mean and variance of X without using direct formula for mean and variance. 7. Consider the joint PDF for the type of customer service X (0 = telephonic hotline, 1 = Email) and of satisfaction score Y (1 = unsatisfied, 2 = satisfied, 3 = very satisfied):
(a) Determine and interpret the marginal distributions of both X and Y. (b) Calculate the 75 % quantile for the marginal distribution of Y. 8. State Monty Hall problem and solve it. 