Let x be a fair dice roll, that is a sample from the uniform distribution in f1; 2; : : : ; 6g. let y be the number of heads in x tosses of a fair coin, that is a coin which is landing heads with probability 1 2 and tails otherwise. we assume the outcome of each coin toss is independent from the outcome of the other coin tosses and from x. a. compute e(y jx = x) for any x = 1; 2; : : : ; 6. b. prove that e(y ) = 1 2 e(x) (1) and derive the value of e(y ). explain intuitively why (1) makes sense.

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the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

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