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Define the term probability. Describe conditional and joint probabilities.
A box includes three white balls W1, W2, W3 and two red balls R1, R2, R3. We remove at arbitrary two balls in succession. Determine the probability that the first removed ball is red and the second
A die is thrown as long as essential for an ace or 6 to turn up. Given that no ace turned up at the first two throws, determine the probability that at least three throws will be essential?
Explain a Latin Square Design. Give suitable example. Write down its advantages. Describe a 22 factorial experiment with 3 replications.
Define Bayes theorem. Describe hypothesis testing problem.
Describe the properties of exponential utility function. Describe the basic aspects of models for individual claim random variables.
What are the properties of Regression Co-efficient? What are the major features of input-output analysis? Compute Karl Pearson’s Co-efficient of Correlation.
Use the method of rank correlation to find out the relationship between scores and IQ.
Compute Yule’s Coefficient of Association between Literacy and Unemployment from the data given below. Total adults: 2,25,000; Literates:50,000; Unemployed: 17,000; Literate and unemployed: 7,
Describe Sen Mrdzyno scheme of sampling. Describe two-stage cluster sampling and state its advantages.
Derive an expression for probability of acceptance to draw OC curve for double sampling plan. Explain parallel series model and obtain corresponding probabilities.
Define Negative Binomial distribution and obtain its probability generating function. Write down the cumulant generating function of Gamma distribution.
Calculate the quartile deviation from the following data: Describe in detail the significance of statistics and its applications in different fields.
Briefly describe the tests of adequacy of Index Number. Give a brief account on the graphical method of measuring secular trend.
Based on following scores (out of 100 possible points), help personnel office of the hospital determine whether the schools differ in quality. Use the Mann-Whitney U test with a 10 percent level of
Mr John buys perishable commodity at Rs 5 each. The profit per unit is Rs 5. This perishable commodity he can keep in his shop for a week and at the end of each week the leftover are sold to a resta
The “School Compost Project” was launched in 2005 in secondary schools in Mauritius with the objective of developing an awareness of how to make use of biodegradable waste in a profitabl
Give an instance of a simple event. Give an instance of a joint event. What is the complement of satisfied with experience.
A survey was conducted by UTM students to find out the monthly consumption of water per household in a city during the recent summer: The data below shows consumption of water from 13 househol
By using the extended Euclidean algorithm, find out the multiplicative inverse of 504 mod 67.
Distinguish carefully between stratified sampling, cluster sampling and quota sampling, stating the advantages and drawbacks of each method.
Write down general procedure for testing of hypothesis. Describe each and every step. Under what condition is it suitable to use a one-tailed test? A two-tailed test?
What do you mean by frequency Polygon and Ogives. How do we draw these? According to Chebyshev’s theorem, between what values must at least 75 percent of the sample observations fall?
State and describe Statistical Process Control. Define various control charts.
Following data represent the life (in months) of 20 UPS fitted to a hospital on February, 25, 2005 : 85 75 66 43 40. Construct frequency distribution with classes 40–49, 50–59, etc. C