Probability distributions using 4 dice

[i_love_science]

Let X denote the largest number shown on the four dice. P(X ≤ x) = (x/6)⁴ , for x = 1,2,3,4,5,6.
Complete the following table:

x	1	2	3	4	5	6
P(X=x)	1/1296	15/1296	65/1296	175/1296	369/1296	671/1296

The values in red are the answers, I don't understand how the answers were found. Thanks.

 

[etotheipi]

Do you know that $P(X \leq x) = P(X = 0) + \dots + P(X=x)$? To find $P(X=x)$ you work out $(x/6)^4$ and then subtract all of the previous probabilities to the left.

 

[DrClaude]

@i_love_science, you will have to make an attempt at a solution if you want more help.

 

[Frabjous]

Try to figure out the answer for x=2. If you can figure it out, it will show you a path to do the higher numbers.