Used in Example 241 to find the probability function of the

Used in Example 2.4-1 to find the probability function of the experiment that records the a mileage the three cars achieve. Use the PMF obtained in part (a) to compute probability that the average gas mileage is at least MPG. 4. The PMF of the sum of two die rolls, found in Example 2.3-13, is (a) For each of the following events specify the outcomes that belong to them, and use relation (2.4.1) to find their probabilities. E_1 = {the sum of the two die rolls is at least 5}. E_2 = {the sum of the two die rolls is no more than 8}. E_3 = E_1 E_2, E_4 = E_1 - E_2, and E_5 = . Recalculate the probability of E_3 using part (1) of Proposition 2.4-2. Recalculate the probability of E_5 using De Morgan\'s first law, the probability of E_3, and part (4) of Proposition 2.4-1. A telecommunications company classifies transmission calls by their duration as brief ( 3 minutes) and by their type as voice (V), data (D^ or fax (F). From an extensive data base, the company has

Solution

Total =36,

E1:{(1,4),(2,3)(3,2),(4,1)}, then P(E1)=4/36. E2:{(1,1),(6,6)}, then P(E2)=2/36. E3:{(1,4),(2,3)(3,2),(4,1),(1,1),(6,6)},then P(E3)=6/36, P(E4)=2/36, E5={null set}, P(E5)=0.