## 1. Consider the following discrete random variable, X.
## x | 6 7 8 9 10 11 12
## P(X = x) | 0.1 0.2 0.3 0.2 0.1 0.05 0.05
## 1.a.
## Calculate the expected value and standard deviation; efficiency counts.
## Hint: not mean() nor sd(); these are population level
## 1.b.
## Randomly sample from the random variable X,
## with samples sizes n = \{10, 100, 1000\}.
## Hint: ?sample; NB the argument prob
## 1.c.
## Calculate the sample mean and sample variance for each random
## sample/size combination.
## Comment on the relative correctness of your three guesses.
## Hint: ?mean; ?sd; these are sample level
## 2. Assume the length of adult male Calponia harrisonfordis is
## normally distributed with mean 18.14 mm and
## standard deviation 1.76 mm. Hint: ?pnorm
## 2.a.
## What is the probability we would find a C. harrisonfordi that is
## shorter than 14.66 mm or longer than 21.66 mm?
## 2.b.
## What is the length of the longest 7.5% of C. harrisonfordis?
## 3. Randomly generate 1001 observations from a normal
## distribution of your choice (pick mean and standard deviation).
## Make a histogram from these observations. Hint: ?rnorm
## 4. An airline charges the following baggage fees: $25 for the first
## bag and $35 for the second. Suppose 54% of passengers have no
## checked luggage, 34% have one piece of checked luggage and 12% have
## two pieces. We suppose a negligible portion of people check more
## than two bags.
## 4.a.
## What is the probability mass function for baggage fees?
## 4.b.
## About how much revenue should the airline expect for a flight of
## 120 passengers?
## 4.c.
##The current exchange rate for one U.S. dollar ($) to one Euro is
## .86. What is the expected revenue in Euros?