Let $X_1, X_2, X_3$ be the numbers that appear when three balanced dice are rolled. Find the expected value of the largest number that you will see.

Question

My attempt: $P[X_i=x] = 1/6$ for $i=1,2,3$.

$E[X] = \sum{xp(x)} = 1×1/6 + 2×1/6 + 3×1/6 + 4×1/6 + 5×1/6 + 6×1/6$

Is my attempt correct?

See here for some nice responses. – jlammy Mar 23 '21 at 15:48 — jlammy, Mar 23 '21 at 15:48

score 2 · Answer 1 · answered Mar 23 '21 at 15:36

No, six has nothing to do with this. What is the probability that the largest element equals $1$ - it is $\frac16^3.$ What is the probability that it is equal to $2?$ It is $\left(\frac26\right)^3 -\left(\frac16\right)^3.$ And so on. So, the expectation is:

$$\sum_{i=1}^6 i \left(\left(\frac{i}6\right)^3 - \left(\frac{i-1}6\right)^3\right).$$

Let $X_1, X_2, X_3$ be the numbers that appear when three balanced dice are rolled. Find the expected value of the largest number that you will see.

1 Answers1