When a fair dice is rolled. 36 equally likely outcomes are possible as shown below.
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let X=Max of numbers shown on the dice
a) Find the probability distribution of X. Give the probabilities rounded to three decimal places.
b) Find the mean and standard deviation of the random variable X.
c) Let A be the event that X is an even number. Find P(A)

Question

When a fair dice is rolled. 36 equally likely outcomes are possible as shown below.
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let X=Max of numbers shown on the dice
a) Find the probability distribution of X. Give the probabilities rounded to three decimal places.
b) Find the mean and standard deviation of the random variable X.
c) Let A be the event that X is an even number. Find P(A)