- #1
toothpaste666
- 516
- 20
Homework Statement
1. Consider selecting at random a student who is among the 15,000 registered for the current semester at a school Let X be the number of courses for which the selected student is registered and suppose that X has probability distribution
x: 1 2 3 4 5 6
f(x): .01 .03 .13 .25 .39 .19
(a) Find the cdf of X.
(b) Find the expected number of courses taken by a student in this semester.
(c) Find the standard deviation of X.
(d) Find the median of this distribution.
The Attempt at a Solution
a)This part I am confused of what they want, since X is not specified. It seems like they already provided me with the cdf
b) this is the summation of the xf(x) 's
(1)(.01) + 2(.03) + 3(.13) + 4(.25) + 5(.39) + 6(.19) = 4.55
c) the variance is the sum of the (x-μ)^2f(x) 's
(1-4.55)^2(.01) + (2-4.55)^2(.03) + (3-4.55)^2(.13) + (4-4.55)^2(.25) + (5-4.55)^2(.39) + (6-4.55)^2(.19)
= 1.1875
and the standard deviation is the square root of that
= 1.09
d) put them in order
.01 .03 .13 .19 .25 .39
the median is (.13 + .19)/2 = .16
unless I am trying to find the median number of courses taken?
in that case
1 2 3 6 4 5
(3+6)/2 = 9/2 = 4.5 courses
I am not that confident I did this right because I didn't use the number of registered students they gave me and I don't think I understood part a)