The birthrates in the U.S for the years 2003-2012 are given in the following table. (The birthrate is the number of live births/1000 population.)
Year 2003 2004 2005 2006 2007
Birthrate 14.7 14.0 14.0 14.2 14.2
Year 2008 2009 2010 2011 2012
Birthrate 14.0 13.8 13.8 13.8 13.7
a) Describe random variable x
b) Find the probability distribution for the random variable x.
a) That would be the years of the birthrates themselves right?
b) Would this be the sum of all the birthrates? 140.2
And then 13.7/140.2, 13.8/140.2.....?
a) disagree
b) don't think so
a) then just the birthrates?
b) 13.7/1000, 13.8/1000 instead?
a) Yes, the random variable x in this case would represent the years for which the birthrates are given, from 2003 to 2012.
b) To find the probability distribution for the random variable x, we need to calculate the probability of each possible outcome. In this case, the possible outcomes are the birthrates for each respective year.
To calculate the probability distribution, we need to divide each birthrate by the sum of all the birthrates. Let's sum up all the birthrates first:
14.7 + 14.0 + 14.0 + 14.2 + 14.2 + 14.0 + 13.8 + 13.8 + 13.8 + 13.7 = 140.2
Now, we can calculate the probability for each birthrate by dividing it by the sum:
P(2003) = 14.7 / 140.2 = 0.1047 (rounded to four decimal places)
P(2004) = 14.0 / 140.2 = 0.0999
P(2005) = 14.0 / 140.2 = 0.0999
P(2006) = 14.2 / 140.2 = 0.1014
P(2007) = 14.2 / 140.2 = 0.1014
P(2008) = 14.0 / 140.2 = 0.0999
P(2009) = 13.8 / 140.2 = 0.0986
P(2010) = 13.8 / 140.2 = 0.0986
P(2011) = 13.8 / 140.2 = 0.0986
P(2012) = 13.7 / 140.2 = 0.0978
The probability distribution for the random variable x is as follows:
P(x=2003) = 0.1047
P(x=2004) = 0.0999
P(x=2005) = 0.0999
P(x=2006) = 0.1014
P(x=2007) = 0.1014
P(x=2008) = 0.0999
P(x=2009) = 0.0986
P(x=2010) = 0.0986
P(x=2011) = 0.0986
P(x=2012) = 0.0978
Each probability represents the likelihood of observing the birthrate in a specific year.