Cover image of Ignou MST-012 Solved Assignment 2023

IGNOU MST-012 Solved Assignment 2023 | MSCAST

Solved By – Narendra Kr. Sharma – M.Sc (Mathematics Honors) – Delhi University

365.00

Share with your Friends

Details For MST-012 Solved Assignment

IGNOU MST-012 Assignment Question Paper 2023

untitled-document-16-9cbde385-ad0a-4c74-864f-362c1a2d74cc
1(a) Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 2 p m 2 p m 2pm2 \mathrm{pm}2pm to 3 p m 3 p m 3pm3 \mathrm{pm}3pm. Suppose they follow the following rules for this meeting:
  • Each of them will reach either on time or 10 minutes late or 20 minutes late or 3 0 3 0 30\mathbf{3 0}30 minutes late or 40 minutes late or 50 minutes late or 1 hour late. All these arrival times are equally likely for both of them.
  • Whoever of them reaches first will wait for the other to meet only for 10 minutes. If within 10 minutes the other does not reach, he/she leaves the place and they will not meet.
    Find the probability of their meeting.
(b) In the study learning material (SLM), you have seen many situations where Poisson distribution is suitable and discussed some examples of such situations. Create your own example for a situation other than which are discussed in SLM. If you denote your created random variable by X X XXX then find the probability that X X XXX is less than 2 .
2(a) In an election there are two candidates. Being a statistician, you are interested in predicting the result of the election. So, you plan to conduct a survey. Using the learning skill of this course answer the following question. How many people should be surveyed to be at least 90 % 90 % 90%90 \%90% sure that the estimate is within 0.03 of the true value?
(b) If X 1 , X 2 , X 3 , X 4 , X 1 , X 2 , X 3 , X 4 , X_(1),X_(2),X_(3),X_(4),dots\mathrm{X}_1, \mathrm{X}_2, \mathrm{X}_3, \mathrm{X}_4, \ldotsX1,X2,X3,X4, be a sequence of continuous random variables such that f x n ( x ) = n 2 e n | x | f x n ( x ) = n 2 e n | x | f_(x_(n))(x)=(n)/(2)e^(-n|x|)f_{x_n}(x)=\frac{n}{2} e^{-n|x|}fxn(x)=n2en|x| then prove that X n p 0 X n p 0 X_(n)rarr^(p)0X_n \stackrel{p}{\rightarrow} 0Xnp0.
  1. Explain the procedure of assigning probability in a continuous world of probability theory.
4(a) If X Gamma ( θ , α ) X Gamma ( θ , α ) X∼Gamma(theta,alpha)X \sim \operatorname{Gamma}(\theta, \alpha)XGamma(θ,α) and Y Gamma ( θ , β ) Y Gamma ( θ , β ) Y∼Gamma(theta,beta)Y \sim \operatorname{Gamma}(\theta, \beta)YGamma(θ,β) be two independent gamma distributions and U = X X + Y U = X X + Y U=(X)/(X+Y)U=\frac{X}{X+Y}U=XX+Y and V = X + Y V = X + Y V=X+YV=X+YV=X+Y then find the distribution of U U UUU.
(b) A hospital specialising in heart surgery. In 2022 total of 2000 patients were admitted for treatment. The average payment made by a patient was Rs 1 , 50 , 000 1 , 50 , 000 1,50,0001,50,0001,50,000 with a standard deviation of Rs 25000 . Under the assumption that payments follow a normal distribution, answer the following questions.
(i) The number of patients who paid between Rs 1 , 40 , 000 1 , 40 , 000 1,40,0001,40,0001,40,000 and Rs 1 , 70 , 000 1 , 70 , 000 1,70,0001,70,0001,70,000.
(ii) The probability that a patient bill exceeds Rs 1 , 00 , 000 1 , 00 , 000 1,00,0001,00,0001,00,000.
(iii) Maximum amount paid by the lowest paying one-third of patients.
\(\operatorname{cosec}^2 \theta=1+\cot ^2 \theta\)

MEV-017 Sample Solution 2023

untitled-document-16-9cbde385-ad0a-4c74-864f-362c1a2d74cc

Question:-01

1(a) Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 2 p m 2 p m 2pm2 \mathrm{pm}2pm to 3 p m 3 p m 3pm3 \mathrm{pm}3pm. Suppose they follow the following rules for this meeting:
  • Each of them will reach either on time or 10 minutes late or 20 minutes late or 3 0 3 0 30\mathbf{3 0}30 minutes late or 40 minutes late or 50 minutes late or 1 hour late. All these arrival times are equally likely for both of them.
  • Whoever of them reaches first will wait for the other to meet only for 10 minutes. If within 10 minutes the other does not reach, he/she leaves the place and they will not meet.
    Find the probability of their meeting.
Answer:

Introduction

Anjali and Prabhat are trying to meet for lunch between 2 pm and 3 pm. They can arrive at seven different times: on time, 10, 20, 30, 40, 50 minutes late, or 1 hour late. Each of these arrival times is equally likely. The first to arrive will wait for 10 minutes for the other. We need to find the probability that they will meet.

Work/Calculations

Step 1: Define the Sample Space

The sample space S S SSS consists of all possible arrival times for Anjali and Prabhat. Since each of them has 7 choices, the total number of outcomes is 7 × 7 7 × 7 7xx77 \times 77×7.
| S | = 7 × 7 = 49 | S | = 7 × 7 = 49 |S|=7xx7=49|S| = 7 \times 7 = 49|S|=7×7=49

Step 2: Identify Favorable Outcomes

A favorable outcome is one where they meet. This can happen if:
  1. Both arrive at the same time: There are 7 such cases (0, 10, 20, 30, 40, 50, 60 minutes late).
  2. One arrives and the other arrives within the next 10 minutes: For example, if Anjali arrives 10 minutes late, Prabhat can arrive either on time or 20 minutes late for them to meet.
To count these, we consider the time difference between their arrivals. The time difference can be 0, 10, 20, 30, 40, 50, or 60 minutes. They will meet if the time difference is 0 or 10 minutes.
  • For a time difference of 0 minutes, there are 7 cases.
  • For a time difference of 10 minutes, there are 6 cases for Anjali arriving first and 6 for Prabhat arriving first, making it 12 cases.
So, the total number of favorable outcomes | E | | E | |E||E||E| is 7 + 12 = 19 7 + 12 = 19 7+12=197 + 12 = 197+12=19.

Step 3: Calculate the Probability

The probability P P PPP of them meeting is given by:
P = | E | | S | P = | E | | S | P=(|E|)/(|S|)P = \frac{|E|}{|S|}P=|E||S|
After calculating, we get the value of P P PPP.
After calculating, we find that the probability of Anjali and Prabhat meeting is 19 49 19 49 (19)/(49)\frac{19}{49}1949.

Conclusion

The probability that Anjali and Prabhat will meet for lunch, given the conditions, is 19 49 19 49 (19)/(49)\frac{19}{49}1949. This takes into account all the possible times they could arrive and the 10-minute waiting time.
\(cos\:2\theta =2\:cos^2\theta -1\)

Frequently Asked Questions (FAQs)

You can access the Complete Solution through our app, which can be downloaded using this link:

App Link 

Simply click “Install” to download and install the app, and then follow the instructions to purchase the required assignment solution. Currently, the app is only available for Android devices. We are working on making the app available for iOS in the future, but it is not currently available for iOS devices.

Yes, It is Complete Solution, a comprehensive solution to the assignments for IGNOU. 

Yes, the Complete Solution is aligned with the requirements and has been solved accordingly.

Yes, the Complete Solution is guaranteed to be error-free.The solutions are thoroughly researched and verified by subject matter experts to ensure their accuracy.

As of now, you have access to the Complete Solution for a period of 1 Year after the date of purchase, which is sufficient to complete the assignment. However, we can extend the access period upon request. You can access the solution anytime through our app.

The app provides complete solutions for all assignment questions. If you still need help, you can contact the support team for assistance at Whatsapp +91-9958288900

No, access to the educational materials is limited to one device only, where you have first logged in. Logging in on multiple devices is not allowed and may result in the revocation of access to the educational materials.

Payments can be made through various secure online payment methods available in the app.Your payment information is protected with industry-standard security measures to ensure its confidentiality and safety. You will receive a receipt for your payment through email or within the app, depending on your preference.

The instructions for formatting your assignments are detailed in the Assignment Booklet, which includes details on paper size, margins, precision, and submission requirements. It is important to strictly follow these instructions to facilitate evaluation and avoid delays.

\(b^2=c^2+a^2-2ac\:Cos\left(B\right)\)

Terms and Conditions

  • The educational materials provided in the app are the sole property of the app owner and are protected by copyright laws.
  • Reproduction, distribution, or sale of the educational materials without prior written consent from the app owner is strictly prohibited and may result in legal consequences.
  • Any attempt to modify, alter, or use the educational materials for commercial purposes is strictly prohibited.
  • The app owner reserves the right to revoke access to the educational materials at any time without notice for any violation of these terms and conditions.
  • The app owner is not responsible for any damages or losses resulting from the use of the educational materials.
  • The app owner reserves the right to modify these terms and conditions at any time without notice.
  • By accessing and using the app, you agree to abide by these terms and conditions.
  • Access to the educational materials is limited to one device only. Logging in to the app on multiple devices is not allowed and may result in the revocation of access to the educational materials.

Our educational materials are solely available on our website and application only. Users and students can report the dealing or selling of the copied version of our educational materials by any third party at our email address (abstract4math@gmail.com) or mobile no. (+91-9958288900).

In return, such users/students can expect free our educational materials/assignments and other benefits as a bonafide gesture which will be completely dependent upon our discretion.

Scroll to Top
Scroll to Top