Solve your Ignou Doubts

) The marketing manager of a company recorded the number of mobiles sold quarterly for which are given in the following table:

Year	Quarter
2018		48	41	60	65
2019		58	52	68	74
2020		60	56	75	78

(i) Find the quarterly seasonal indexes for the mobile sold using the ratio to trend method.
(ii) Do seasonal forces significantly influence the sale of mobile? Comment.
(iii) Also find the deseasonalised values. 

Consider the time series model

where 

(i) Is this a stationary time series?
(ii) What are the mean and variance of the time series?
(iii) Calculate the autocorrelation function.
(iv) Plot the correlogram. 

At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in seconds:

(i) Use the data to construct control charts for mean and comments about the
process. If process is out of control, then calculate the revised control limits.

(ii) Construct the CUSUM chart when the process is under control and draw the conclusion about the process.

(iii) If the specification limits as the 8±2, then calculate the process capability index Cpk and impetrate the result.

(iv) Also find the percentage of calls lie outside the specification limits assuming that calls follow the normal distribution. 

The failure data for 40 electronic components is shown below:

Estimate the reliability, cumulative failure distribution, failure density and failure rate functions.

A system has seven independent components and reliability block diagram of it shown as follows:

Find reliability of the system.

An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are nonconforming, the lot will be accepted. Otherwise, a second sample of size 8 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second sample. Also AQL and LTPD are 0.05 and 0.10 respectively. Let incoming quality be 4%.

(i) What is the probability of accepting the lot at the first sample?
(ii) What is the probability of accepting the lot at the second sample? 

A manufacturer of men’s jeans purchases zippers in lots of 500. The jeans manufacturer uses single-sample acceptance sampling with a sample size of 10 to determine whether to accept the lot. The manufacturer uses c = 2 as the acceptance number. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8% nonconforming zippers are not acceptable. Find

(i) Probability of accepting a lot of incoming quality 0.04.
(ii) Average outing quality (AOQ), if the rejected lots are screened and all defective zippers are replaced by non-defectives.
(iii) Average total inspection (ATI). 

Differentiate between the autoregressive and moving average models of time series.

State whether the following statements are True or False. Give reason in support of your answer:

(i) The R- chart is suitable when subgroup size is greater than 10.

(ii) In single sampling plan, if we increase acceptance number then the OC curve will be steeper.

(iii) If the effect of summer and winter is not constant on the sale of AC then we use the additive model of the time series.

(iv) If a researcher wants to find the relationship between today’s unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.

(v) A system has four components connected in parallel configuration with
reliability 0.2, 0.4, 0.5, 0.8. To improve the reliability of the system most, we
have to replace the component which reliability is 0.2. 

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 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 and Rs 1,70,000.
(ii) The probability that a patient bill exceeds Rs 1,00,000.
(iii) Maximum amount paid by the lowest paying one-third of patients

If X ~ Gamma , and Y ~ Gamma , (θ α) (θ β) be two independent gamma distributions and

    and    then find the distribution of U. 

Explain the procedure of assigning probability in a continuous world of probability theory

Let (Ω, , ) be a probability space and  be a sequence of independent and identically distributed (i.i.d.) random variables from the uniform distribution on the interval [12, 20]. If Xn denotes the sample mean of the first n random variables of the sequence

 and  Find the value of 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% sure that the estimate is within 0.03 of the true value?

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 those that are discussed in SLM. If you denote your created random variable by X then find the probability that X is less than 2.

Suppose two friends Anjali and Prabhat trying to meet for a date to have lunch say between 2 pm to 3 pm. 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 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.

No.3. Elucidate women writers and market deconstructing this Picasso painting.

No. 2. Critically analyse censorship and queer cinema after pandemic. (You can use Block 2 as reference)

No.1. Discuss gender and performance using this image: (You can use Block 3 and 4 as reference)

Elucidate on body and violence from gender perspective using this image. (Refer to Block 3)

Critically analyze the debates of histories and forms of life narratives of Indian authors from a gender perspective. (Refer to Block 4)

(i) Cluster Computing
(ii) Master Slave Kernel
(iii) System Deadlock
(iv) Parallel Random Access Machine
(v) Instruction Level and Loop Level
(vi) Parallelism

What are the problems encountered in superscalar architecture? Discuss.

Define 8 x 8 Benz network of 4 stage in detail.

Explain odd-even transposition sorting method. Provide an example to understand the concept.

Solve the matrix multiplication problem using the parallel models.

Explain the algorithm for matrix multiplication for parallel computational model. What is its complexity?

Discuss the performance and issues factor in pipelining.

Discuss the performance and issues factor in pipelining.

Discuss the design issues of interconnection network in detail.

Explain the various classifications of parallel computers in detail.

What are residual plots? Discuss the utility and disadvantage of residual plots.

Briefly discuss the following with a suitable example:

(i) Non Linear Regression

(ii) Acceptance Rejection method

1000 light bulbs with a mean life of 120 days are installed in a new factory and their length of life is normally distributed with standard deviation of 20 days.

 (i) How many bulbs will expire in less than 90 days?

(ii) If it is decided to replace all the bulbs together, what interval should be allowed between replacements if not more than 10% should expire before replacement?

The length of metallic strips produced by a machine has mean 100 cm and variance 2.25 cm. Only strips with length between 98 and 103 cm are acceptable. What proportion of strips will be acceptable? You may assume that the length of a strip has a Normal Distribution.

In the table below, the value of y are consecutive terms of a series of which 23.6 is the sixth term. Find the first and tenth terms of the series using Newton’s forward interpolation method.

A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 18 and that of wife’s selection is ¼. What is the probability that:
(i) Both of them will be selected
(ii) Only one of them will be selected
(iii) None of them will be selected.

Use the Jacobi method to solve the following system of equations: 
3x + 4y + 15z = 54.8
x + 12y + 3z = 39.66
10x + y — 2z = 7.74

Solve the following system of equations by using the Gauss Elimination method: (8 Marks)
 x + 2y + z = 3
2x + 3y + 3z = 10
3x y + 2z = 13

Calculate the value of the integral

(i) Simpson's 1/3 rule,

(ii) Simpson's 3/8 rule.

Use Regula-Falsi method to find the roots of the equation f(x) =x³ + x – 1.

Write a program in Prolog to find and print prime numbers between 50 to 200.

What is the difference between Knowledge and Intelligence? Enumerate the various knowledge representation schemes, giving a brief description for each scheme.

Write BFS algorithm. Use the BFS to search the goal node . Show each step of the algorithm.

What is Means-Ends Analysis? How is Means-Ends Analysis used as a problem solving technique?

Define fuzzy inference system? What are the main steps in Fuzzy inference system? Make an inference system for food management system.

What are Semantic Nets? Briefly discuss the utility of semantic nets in knowledge management. Give suitable example in support of your answer.

What is Prenex Normal Form (PNF). Write the steps to transform a Well-Formed Formula (WFF) into PNF. Transform Ɐx(Q(x) →(ⱻx) R(x, y)).

Write a program in LISP to calculate the area of the circle, whose radius is given by the user. Write proper comments to enhance readability of your code.

What are Expert Systems? Briefly discuss the various categories of software tools, used for the development of expert systems.