Following data presents a population of 10 clusters of size 3 each. Each cluster represents a bunch of students of standard IV in a school. The marks obtained by students in a competitive test (out of 75 marks) have been shown in the data set. Find the Relative Efficiency (R.E.) of the Cluster Sampling with respect to the Simple Random Sampling without Replacement scheme:

 In a population of size 500, the population mean of the auxiliary variable X was observed to be 834.00. On the basis of a sample of size 40, the following sample values were obtained:

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$y = 740.00; \bar{x} = 865.00; s_y^2 = 9560.00; s_x^2 = 15300.00; s_{yx} = 30540.2.$

Obtain the values of the regression estimate and the ratio estimate of the population mean as obtained on the basis of the sample drawn. $\quad \quad \quad \quad \quad \quad \quad \quad (08)$

 In a population of size 500, the population mean of the auxiliary variable X was observed to be 950.00. On the basis of a sample of size 30, the following sample values were obtained:

Obtain the value of the Ratio estimate of population mean as obtained on the basis of the sample drawn. Also, find the estimated value of the Sample Mean Squared Error of the estimate.

State whether the following statements are true or false and also give the reason in support of your answer: 
a) In Two-Stage Sampling if , it becomes the Cluster Sampling.
b) Among all the members of the General Class of the estimators only Product estimator is an unbiased estimator of the Population mean.
c) With the following parameters , an Incomplete Block Design is found to be a Balanced Incomplete Block Design.
d) a 2³ Factorial design is One-half fractional factorial design of a 2⁶ full factorial design.
e) If M_i and  are correlated, the Cluster estimator  becomes an unbiased estimator of the Population Mean.

Write a Python program using NumPy to
(i) Create following two matrices P and Q with following elements.
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(ii) Compute the (a) Addition, (b) Multiplication, (c) Determinant and (d) Inverse of these matrices.
(iii) Combine the given matrices row-wise and determine the transpose of the combined matrix.
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Would you like me to write the actual Python code to solve these problems for you?

What are different ways to create a NumPy array? Explain any two with examples.

Describe any two Python libraries used for data visualization.

 Describe the while loop with an example program.

Explain how file handling works in Python for text files. Mention different file modes, and a short description of read(), readline() and write().

 Describe the key features of Spyder.

Write a Python program to accept a list of tuples (product_name, price) for 5 items from the user, then sort the list by price in descending order using a function.

Find and correct the error in the following code.

import numpy as np

arr = np.array[4, 5, 6]

print(arr)

Write the output of the following Python code.

nums = [10, 20, 30, 40, 50]

print(nums[-2])

Consider the following table for the connections between the input neurons and the hidden layer neurons

 If the input vectors are  and initial values of three weight vectors are , then calculate the resulting weight found after training the competitive layer with Kohonen's rule and a learning rate  of 0.5 on the input-series in order I₁, I₂ and I₃. 

What is the role of loss function in machine learning algorithms? Explain any two commonly used loss functions in machine learning algorithms.

Supervised Learning,
Unsupervised learning,

Cultural Identity

Translation and New Political World Order

Elaborate Indian Multiculturalism in Global context.