Which of the following are valid probability distribution functions?
(a)Pr[X =
x\ = x/2,
for ÷ = - 1 , 0 , 1 , 2.
(b)Pr[X = x] = (6 - 2x)/14, for ÷ = 0 , 1 , 2 , 3 .
(c)
Pr
[X =
÷] = (÷2 - ÷ + l ) / 4 6 , for ÷ = 0 , 1 , . . . , 5 .
Suppose that a researcher would like to know the mean height of female high
school students. The researcher randomly selects female high school students who
are in attendance at school on a particular day and measures their heights. Suppose
that all female high school students who play basketball are competing at a basketball
tournament on this particular day and so are not eligible to be included in the sample.
(a) Is the researcher's sample a random sample of the population of female high
school students? Why or why not?
(b) Suppose that the mean height of non-basketball-playing female high school
students is 64 inches and the mean height of basketball-playing female high
school students is 69 inches. Further, assume that 10% of females play basketball
in high school. What is the population mean height of female high
school students? What is the mean height of the population that is actually
being sampled by the researcher on this particular day?