IGNOU MST 3 SOLVED ASSIGNMENT 2025

Ques 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(ゆす。,

c) If events  are mutually exclusive and exhaustive then will be greater than 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(SE)-1.

(e) If X is a random variable having range set (0, 1, 2, 3) then the set (xS:X(x)0 is an event having at least one outcome of the random experiment.

Ques 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.

Ques 3.

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

Ques 4.

Show that

f(x1,2, 1,2,3,4,5, is a valid PMF for a discrete random variable. Also find out its CDF.

Ques 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.

Ques 6.

Random variable X follows Beta distribution with parameters a 3, b-2 and has pdf f(x12x(1x),0x1 10,otherwise Find (1) CDF of X (ii) Pdf 

is a valid PMF for a discrete random variable. Also find out its CDF.

Ques 7.

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.

Ques 8.

Random variable X follows Beta distribution with parameters a 3, b-2 and has pdf f(x12x(1x),0x1 10,otherwise Find (1) CDF of X (ii) P[0

Random variable X follows Beta distribution with parameters a=3, b = 2 and has pdf

Find (1) CDF of X (ii) P(0<X<1/2] (iii) mean and variance of X without using direct formula for mean and variance.

Ques 9.

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.

(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.

Ques 10.

State Monty Hall problem and solve it.

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