SOLUTION: (a) Find the CDF of X where X is a continuous random variable with pdf f(x) = 1/3 for the interval 0 to 1 and 2/3 for the interval 1 to 2. (b) Find the median of random variable

Algebra ->  Probability-and-statistics -> SOLUTION: (a) Find the CDF of X where X is a continuous random variable with pdf f(x) = 1/3 for the interval 0 to 1 and 2/3 for the interval 1 to 2. (b) Find the median of random variable      Log On


   

Question 349491: (a) Find the CDF of X where X is a continuous random variable with pdf f(x) = 1/3 for the interval 0 to 1 and 2/3 for the interval 1 to 2.
(b) Find the median of random variable X.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a) Integrate to find the CDF.
PDF=%281%2F3%29 0%3C=x%3C1
PDF=%282%2F3%29 1%3C=x%3C=2
Integrating,
CDF=%281%2F3%29x%2BC%5B1%5D 0%3C=x%3C1
CDF=%282%2F3%29x%2BC%5B2%5D 1%3C=x%3C=2
Solve for the constants using conditions,
CDF%280%29=0
%281%2F3%29%280%29%2BC%5B1%5D=0
C%5B1%5D=0
.
.
.
CDF%282%29=1
%282%2F3%29%282%29%2BC%5B2%5D=1
C%5B2%5D=-1%2F3
.
.
.
CDF=%281%2F3%29x 0%3C=x%3C1
CDF=%282%2F3%29x-1%2F3 1%3C=x%3C=2
.
.
.
b) Median=1