Question

Suppose you roll n ≥ 1 fair dice. Let X be the random variable for the sum of their values, and let Y be the random variable for the number of times an odd number comes up. Prove or disprove: X and Y are independent.

Answer 1

Answer:

X and Y are stochastically dependent RVs .

Step-by-step explanation:

Let ,

X = sum of the values that come up after throwing n (≥ 1) fare dice.

Y = number of times an odd number come up.

Let, n = 3

then, P(X =6) = p (say) clearly 0 < p < 1

and P (Y = 3) = $\frac{1}{8}$

And,

P( X = 6, Y = 3) = 0  ≠ $P(X = 6) \times P(Y= 3)$

Hence, X and Y are stochastically  dependent  RVs