NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Mean and variance of Linear combinations of DRV

## Interactive practice questions

The expected value of a discrete random variable is $E\left(X\right)=4.3$E(X)=4.3

a

Calculate $2E\left(X\right)$2E(X).

b

Calculate $E\left(2X\right)$E(2X).

c

Calculate $E\left(X-1\right)$E(X1).

d

Calculate $E\left(4X+1\right)$E(4X+1).

e

Solve for the value of $n$n such that $E\left(nX+3\right)=11.6$E(nX+3)=11.6.

Easy
Approx 3 minutes

The variance of a discrete random variable is given by $V\left(X\right)=3.24$V(X)=3.24

Consider the discrete random variable given below, where $E\left(X\right)$E(X) is the expected value and $V\left(X\right)$V(X) is the variance.

The table below represents the distribution of a discrete random variable, where $E\left(X\right)$E(X) is the expected value, $V\left(X\right)$V(X) is the variance and $S\left(X\right)$S(X) is the standard deviation.

### 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