In a game, Jim throws three darts at a board. This is called a 'turn'. The centre of the board is called the bull's-eye. The random variable $$$X$$$ is the number of darts in a turn that hit the bull's-eye. The probability distribution of $$$X$$$ is given in the following table. It is given that $$$\mathrm{E}(X)=0.55$$$. Find $$$\operatorname{Var}(X)$$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_53 Year：2021 Question No：6(b)

Answer:

$\operatorname{Var}(X)=$ their $0.3+4 \times$ their $0.05+9 \times 0.05-0.55^{2}$
$0.6475\left[\frac{259}{400}\right]$

5.4.1 draw up a probability distribution table relating to a given situation involving a discrete random variable X, and calculate E(X) and Var(X)