-Two restaurants, Epicurean Eats and Dino’s Diner, operate in the same neighborhood. Epicurean Eats is a higher-priced, gourmet establishment and Dino’s serves inexpensive, quick meals. The number of customers per hour varies according to the economy. When the economy is strong, people are willing to spend more money eating out. Using the following probability distribution for customer traffic at the two restaurants, answer the questions below.
Customers/Hour
Economy Prob Epicurean Eats (EE) Dino’s Diner (DD)
Strong 0.3 30 10
Fair 0.5 25 45
Weak 0.2 20 50
1:Cov (EE, DD) ?
2:Correlation Coefficent (EE, DD)?
| EE | ||||||
| Scenario | Probability | Customer/hr | =Customer/hr * probability | Actual Customer/hr-expected Customer/hr | (A)^2* probability | |
| Strong | 0.3 | 30 | 9 | 4.5 | 0.0006075 | |
| Fair | 0.5 | 25 | 12.5 | -0.5 | 0.0000125 | |
| Weak | 0.2 | 20 | 4 | -5.5 | 0.000605 | |
| Customer/hr= | sum of weighted Customer/hr = | 25.5 | Sum=Variance EE= | 0.00123 | ||
| Standard deviation of EE% | =(Variance)^(1/2) | 3.5 | ||||
| DD | ||||||
| Scenario | Probability | Customer/hr | =Customer/hr * probability | Actual Customer/hr-expected Customer/hr | (A)^2* probability | |
| Strong | 0.3 | 10 | 3 | -25.5 | 0.0195075 | |
| Fair | 0.5 | 45 | 22.5 | 9.5 | 0.0045125 | |
| Weak | 0.2 | 50 | 10 | 14.5 | 0.004205 | |
| Customer/hr= | sum of weighted Customer/hr = | 35.5 | Sum=Variance DD= | 0.02823 | ||
| Standard deviation of DD% | =(Variance)^(1/2) | 16.8 | ||||
| Covariance EE DD: | ||||||
| Scenario | Probability | Actual Customer/hr%-expected Customer/hr for A(A) | Actual Customer/hr -expected Customer/hr For B(B) | (A)*(B)*probability | ||
| Strong | 0.3 | 4.5 | -25.5 | -0.0034425 | ||
| Fair | 0.5 | -0.5 | 9.5 | -0.0002375 | ||
| Weak | 0.2 | -5.5 | 14.5 | -0.001595 | ||
| 1. Covariance=sum= | -0.005275 | |||||
| 2. Correlation A&B= | Covariance/(std devA*std devB)= | -0.897092951 | ||||
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