Identifying the set of possible values

Question

Identify the set of possible values for each random variabl. ( make a reasonable estimate based on experienc, where necessary.) 

 

a: the number of hearts in a five card hand drawn from a deck of 52 cards that contains 13 hearts in all.

 

 

b: the number of pitches made by a starting pitcher in a Major League Baseball game.

 

 

c: the number of breakdowns of city buses in a large city in one week.

 

 

d: the distance a renatal car rented on a daily rate is driven each day.

 

 

 

e: the amount of rainfall at an airport next month.

 

 

Answer 1

a) draw 5 cards from 52 card deck with 13 hearts. how many hearts do you expect to get??

one out of 4 chance of a heart for 1 card

2nd has chance of 12/51

3rd 11/50

4th 10/49

5th 9/48

1/4 + 12/51 + 11/50 + 10/49 + 9/48 = about 1.06 hearts = about 1 heart

for a 4 card draw, you'd expect 1 heart, on average, as 1/4 of the deck are hearts. 5 card draw more than 1, 8 card draw you'd expect 2 hearts 6 card draw 1.5 hears. 5 card seems like 1 1/4 hearts expected

go with 1.25 hearts. But that confuses odds with replacement and without replacement. Go with 1.09 hearts expected as most draws are without replacement

b) pitches in one inning >/= 3 as he could throw to 3 batters who all swing at first pitch and fly out

or max sky's the limit, as in the movie Sandlot (good movie, as are its sequels) where the boy keeps hitting foul balls at every pitch the girl throws. so taking average of max and min won't work. Unless the pitcher gets relieved by a relief pitcher as the starting pitcher's arm is too tired to continue. so there is a max about 30 or 40+ and average about 15

c) average is less than 1 breakdown per week. well maintained bus rarely breaks down

d) on average about 100 to 250 miles per day for car rentals, but varies depending on rental charges. Unlimited mileage car rentals have far more miles

e) rainfall at airport in one month is 3 to 5 inches in a major hub like Atlanta. depends on geography, Seattle gets a lot of rain, relative to other places. Desert areas close to 0 inches