TUTORIAL 3
1. Classify the following random variables as discrete or continuous:
๐ฟ: the number of automobile accidents per year in Virginia.
๐ : the length of time to play 18 holes of golf.
๐ด: the amount of milk produced yearly by a particular cow.
๐ต: the number of eggs laid each month by a hen.
๐ท: the number of building permits issued each month in a certain city.
๐ธ: the weight of grain produced per acre.
2. Determine the value c so that each of the following functions can serve as a probability
distribution of the discrete random variable X:
a. ๐(๐ฅ) = ๐(๐ฅ2 + 4),๐๐๐ ๐ฅ = 0,1,2,3;
b. ๐(๐ฅ)=๐(2
๐ฅ)(3
3โ๐ฅ),๐๐๐ ๐ฅ=0,1,2.
3. The shelf life, in days, for bottles of a certain prescribed medicine is a random variable
having the density function
๐(๐ฅ)={20000
(๐ฅ+100)3, ๐ฅ>0
0 , ๐๐กโ๐๐๐ค๐๐ ๐
Find the probability that a bottle of this medicine will have a shell life of
a. at least 200 days;
b. anywhere from 80 to 120 days.
4. The total number of hours, measured in units of 100 hours, that a family runs a vacuum
cleaner over a period of one year is a continuous random variable ๐ that has the density
function
๐(๐ฅ)={ ๐ฅ, 0<๐ฅ<1
2โ๐ฅ, 1โค๐ฅ<2
0, ๐๐๐ ๐๐คโ๐๐๐
Find the probability that over a period of one year, a family runs their vacuum cleaner
a. less than 120 hours;
