2.7 Statistical distributions

The random variable $X\,$ has the following probability distribution.


$x$	1	2	3	4	5
$P (X = x)$	$k$	$k2\displaystyle \frac{k}{2}$	$k3\displaystyle \frac{k}{3}$	$k4\displaystyle \frac{k}{4}$	$k5\displaystyle \frac{k}{5}$

where $k\,$ is a constant.

a.

Find the value of $k$ .

[3]

b.

The random variables $X_1\,$ and $X_2\,$ are independent and each have the same distribution as $X$ . Find $P(X_1 + X_2 = 7)$

[4]

The random variable $X\,$ has the following probability distribution.


$x$	1	2	3	4	5
$P (X = x)$	$k$	$k2\displaystyle \frac{k}{2}$	$k3\displaystyle \frac{k}{3}$	$k4\displaystyle \frac{k}{4}$	$k5\displaystyle \frac{k}{5}$

where $k\,$ is a constant.

a.

Find the value of $k$ .

[3]

b.

The random variables $X_1\,$ and $X_2\,$ are independent and each have the same distribution as $X$ . Find $P(X_1 + X_2 = 7)$

[4]

2.7 Statistical distributions Questions