# IGNOU MST-003 Solved Assignment 2022

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## IGNOU MST-003 Solved Assignment 2022

MST-003 Solved Assignment is an e-book 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 MST-003 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 MST-003 Sample Solution 2022

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## IGNOU MST-003 Solved Assignment 2022

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## (Probability Theory)

MST-003: Probability Theory

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

$$\left(-\infty \:,\infty \:\right)$$​.
(c) If events E1, E2, E3, E4,….., En are mutually exclusive and exhaustive then ​$$P\left(E_1\cup E_2\cup \:E_3\cup ……..E_n\right)$$​will be greater than ​$$\frac{1}{2}$$​but less than 1.

(d) If S is sample space of a random experiment and E is an event defined on this sample space then P(S|E) = 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 5-card 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

$$f\left(\:x\right)\:=\begin{Bmatrix}12x^2\left(\:1-x\right)\::0\:<x\:<1\\ 0;\:otherwise\end{Bmatrix}$$

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):

 Y X 1 2 3 0 0 1/2 1/4 1 1/6 1/12 0

(a) Determine and interpret the marginal distributions of both X and Y.

(b) Calculate the 75 % quantile for the marginal distribution of Y.
(c) Determine and interpret the conditional distribution of satisfaction level for X = 1.
(d) Are the two variables independent?
(e) Calculate and interpret the covariance of X and Y.

8. State Monty Hall problem and solve it.

Insert math as
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