New Zealand
Level 8 - NCEA Level 3

# Measures of Variability of Discrete Random Distribution

## Interactive practice questions

Consider the table.

 $x$x $P$P$($($X=x$X=x$)$) $0$0 $1$1 $2$2 $3$3 $4$4 $0.12$0.12 $0.15$0.15 $0.22$0.22 $0.23$0.23 $0.28$0.28
a

Does the table represent a discrete probability distribution?

Yes

A

No

B

Yes

A

No

B
b

Calculate $E\left(X\right)$E(X).

c

Calculate the variance of $X$X.

d

Hence calculate the standard deviation.

Easy
Approx 6 minutes

Consider the graph drawn below of a discrete probability distribution.

Consider the probability distribution shown.

### 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