Decision Science
1. The table mentioned below shows the “Gross Production of Energy by Two Sources in India from 2010-11 to 2015-16”.
Adopt Exponential Smoothing Method. Consider the Alpha (α) values 0.2, 0.5, 0.7 and find out the one that is comparatively good for the prediction.
Forecast the value for year 2016-17.
| Year | Coal – (Million Tones) | Lignite – (Million Tones) |
| 2010-11 | 532.7 | 37.73 |
| 2011-12 | 539.95 | 42.33 |
| 2012-13 | 556.4 | 46.45 |
| 2013-14 | 565.77 | 44.27 |
| 2014-15 | 609.18 | 48.27 |
| 2015-16 | 639.23 | 43.84 |
Source: Open Government Data (OGD) Platform India
2. Consider the following Decision alternative for the Raman Pahwa, he wants to invest in stocks, and thought about two situations about tomorrow’s market condition. The figures (in INR) in the following table exhibit profit per unit of stock-investment.
payoff table:
| Favorable market | Unfavorable market | |
| Lakshmi pvt ltd | 55 | 26 |
| Mehta Groups of industries | 43 | 38 |
| Surya | 29 | 43 |
| LT energy | 15 | 51 |
1. Draw the decision tree
2. If we assign the following probabilities to the states of nature, then determine the EMV decision.
P(s1) = .4 P(s2) = .1 P(s3) = .3 P(s4) = .2
3.a. The proportion of eligible voters in the next corporation election (in tumkur) who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for the incumbent? Write your conclusion.
3.b. The top-selling Amar tire is rated 70,000 KMs, which means nothing. In fact, the distance the tires can run until they wear out is a normally distributed random variable with a mean of 82,000 KMs and a standard deviation of 6,400 KMs.
What is the probability that a tire wears out before 70,000 KMs?
What is the probability that a tire lasts more than 100,000 KMs?
Note: You may use Z-table for this.
Z-table link- Normal Table.xls