Methods2025 Exam 1 · Q4Tech-free4 marks

Discrete probability distribution with parameter k

The probability distribution for the discrete random variable $X$ is given in the table below, where $k$ is a positive real number.

| $x$ | $0$ | $1$ | $2$ | | |---|---|---|---|---| | | | | | |

Show that $k = 10$ or $k = 15$ .

2 marks

Hints, answer checking and worked solutions come with a Season Pass.

b.i.

Let $k = 15$ .

Find $\Pr(X > 1)$ .

1 mark

Hints, answer checking and worked solutions come with a Season Pass.

b.ii.

Find $\operatorname{E}(X)$ .

1 mark

Hints, answer checking and worked solutions come with a Season Pass.