$X$ takes the values 1, 2 and 3. Which of these can be its probability distribution?

P(X = x) = \frac{x}{3}

Correct answerYour answer

P(X = x) = \frac{x - 2}{2}

Correct answerYour answer

P(X = x) = \frac{x}{6}

Correct answerYour answer

P(X = x) = \frac{1}{x}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A distribution needs every probability from 0 to 1 and a total of 1.
$\frac{1}{6} + \frac{2}{6} + \frac{3}{6} = 1$ . The others total 2, have $-\frac{1}{2}$ at $x = 1$ , or total $\frac{11}{6}$ .

Worth noting

$\frac{x - 2}{2}$ totals $-\frac{1}{2} + 0 + \frac{1}{2} = 0$ , and it has a negative value.

Ten questions from Random Variables, Expectation & Variance, at your own pace.

Ten questions from Random Variables, Expectation & Variance, at your own pace.

XXX takes the values 1, 2 and 3. Which of these can be its probability distribution?