Question

State whether the following is True or False :

X is the number obtained on upper most face when a die is thrown then E(X) = 3.5.

Options

• True

• False

Answer 1

X : number obtained on upper most face.
∴ Possible values of X are {1, 2, 3, 4, 5, 6}

∴ P(X = x) = `(1)/(6)`, for x = 1, 2, ..., 6

∴ E(X) = \[\sum\limits_{x=1}^{6} x\text{P}(x)\]

= `(1 xx 1)/(6) + (2 xx 1)/(6) + (3 xx 1)/(6) + (4 xx 1)/(6) + (5 xx 1)/(6) + (6 xx 1)/(6)`

= 3.5 is True.