New Zealand
Level 8 - NCEA Level 3

# Constructing Discrete Probability Distribution

## Interactive practice questions

Danielle records her team's winning or losing margins over $10$10 games of the hockey season, with winning margins recorded as positive values and losing margins as negative values. The margins were recorded below.

 $X$X $-1$−1 $4$4 $2$2 $3$3 $1$1 $2$2 $4$4 $-1$−1 $2$2 $1$1
a

Let $X$X be the margin of a given game. Summarise this data in a frequency table.

$X$X Frequency
$-1$1 $\editable{}$
$1$1 $\editable{}$
$2$2 $\editable{}$
$3$3 $\editable{}$
$4$4 $\editable{}$
b

Hence, complete this table for the discrete probability distribution for $X$X.

 $x$x $P\left(X=x\right)$P(X=x) $-1$−1 $1$1 $2$2 $3$3 $4$4 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
Easy
Approx 3 minutes

A fair standard die is thrown and the number of dots on the uppermost face is noted.

Let $X$X be the number of dots on the uppermost face.

A fair standard die is rolled and the number of dots on the visible faces (that is, the faces which are not on the ground) is noted.

Let $W$W be the number of dots that can be seen on the visible faces.

A fair standard die is thrown onto the ground and the number of visible odd-numbered faces is noted.

Let $Y$Y be the number of visible odd-numbered faces.

### Outcomes

#### S8-4

Investigate situations that involve elements of chance: A calculating probabilities of independent, combined, and conditional events B calculating and interpreting expected values and standard deviations of discrete random variables C applying distributions such as the Poisson, binomial, and normal

#### 91586

Apply probability distributions in solving problems