A fair die is rolled twice Let X be the minimum of two rolls

A fair die is rolled twice. Let X be the minimum of two rolls. a) Find the distribution of X. b) Find the expected value of X.

distribution of probability

for x=6 one combination (6,6)

for x=5 three combination (5,5), 56 , 65

for x=4 five combination 44,45,54,46,64

for x=3 seven combination 33,34,43,35,53,36,63

for x=2 nine combination 22,23,32,24,42,25,52,26,62

for x=1 eleven combination 11,12,21,13,31,14,41,15,51,16,61

P(x=1) = 11/36

P(x=2) = 9/36

P(x=3) = 7/36

P(x=4) = 5/36

P(x=5) = 3/36

P(x=6) = 1/36

Expected value = sum( value * probability) = (11/36 * 1 + 9/36 * 2+.......+1/36 * 6)=2.53