Two breakfast food manufacturers X and Y are competing for an increase market share. The payoff matrix, shown in the following table, describes the increase in the market share for X and decrease in the market share of Y.
| X | Y | |||
| Give Coupons | Decrease Price | Maintain Present Strategy | Increase Advertising | |
| Give Coupons | 10 | -10 | 20 | 5 |
| Decrease Price | 30 | 5 | 60 | 15 |
| Maintain Present Strategy | -30 | 10 | 0 | 30 |
| Increase Advertising | 10 | -15 | 35 | 5 |
(i) Check whether saddle point exit or not.
(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.
The first step is to search for a saddle point. There is no saddle point in the problem. The second step is to observe if the pay off matrix can be reduced in size by rules of dominance. Since each element of second row is less than the corresponding elements of second row, second row is dominated by first row because payoffs are less attractive for firm A. Thus after deleting the second ________ _______ _________ _________ ______ _____ _____ ___ _______ _______ ____ _______.
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(b) A coal-fired power plant is considering two different systems for pollution abatement. The first system has reduced the emission of pollutants to acceptable levels 68 percent of the time, as determined from 200 air samples. The second, more expensive system has reduced the emission of pollutants to acceptable levels 76 percent of the time, as determine from 250 air samples. If the expensive system is significantly more effective than the inexpensive system in reducing pollutants to acceptable levels, then the management of the power plant will install the expensive system. To decide that
(i) State null and alternative hypotheses
(ii) Name the test which is suitable in this situation and why?
(iii)Calculate the value of test statistic and critical value.
(iv)Which system will be installed if management uses a significance level 0.01 in making decision?
State whether the following statements are true or false and also give the reason in support of your answer:
b) In cluster sampling the variance within clusters is greater than the variance between
clusters.
c) While analysing the data of a 5 × 5 Latin Square design the error d.f. is equal to 12.
d) In a Two way analysis of variance with 4 blocks & 4 treatments the degree of freedom
for the total variation is 15.
e) Suppose a random number generated by Middle. Square Method is 16, then the next
random number will be 44.
In a population of size N = 5, the values of the population characteristics are 1, 3, 5, 7, 9, a sample of size 2 is drawn. Verify that is an unbiased estimate of
and V(
) is equal to
A coin is biased so that heads appears with probability 2/3 and tails with probability 1/3. This coin is tossed three times. If X denotes the number of heads occurring and Y denotes the number of tails that occur up to the first head, if any, that appears, then determine
i) the joint probability mass function of X and Y.
ii) marginal probability mass functions of the random variables
iii)
The solution to a transportation problem with 3-rows (supplies) and 3-columns (destinations) is feasible if number of positive allocations is 6
If the coefficient of determination is 0.833, the number of observations and independent variables are 12 and 3, respectively, then Adjusted R2 will be 0.84.
Roll two fair dice, one red and one blue, and consider the events:
A: “The red die lands on 4”,
B: “The sum on the dice is 9” and
C: “The blue die lands on an odd number”.
Determine which pairs of events are independent.