Suppose a fair die is rolled twice and that X is the absolute value of the difference of the two rolls. Find the PMF and the CDF of X and plot the CDF. Find the median of X. Is the median unique?
a) PMF: P(X=0)=1/6, P(X=1)=2/3, P(X=2)=1/6; CDF: F(x)=0 for x<1, 1/3 for 1≤x<2, 1 for x≥2; Median: 1; Yes
b) PMF: P(X=0)=1/3, P(X=1)=1/3, P(X=2)=1/3; CDF: F(x)=0 for x<1, 1/2 for 1≤x<2, 1 for x≥2; Median: 1; Yes
c) PMF: P(X=0)=1/6, P(X=1)=1/2, P(X=2)=1/3; CDF: F(x)=0 for x<1, 5/6 for 1≤x<2, 1 for x≥2; Median: 1; Yes
d) PMF: P(X=0)=1/3, P(X=1)=1/2, P(X=2)=1/6; CDF: F(x)=0 for x<1, 2/3 for 1≤x<2, 1 for x≥2; Median: 1; Yes
