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.

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) =

And,

P( X = 6, Y = 3) = 0  ≠

Hence, X and Y are stochastically  dependent  RVs

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation:

step-by-step explanation:

the true ones are a b and d