QUESTION ONE

a$)$ Describe how a perceptron learning algorithm works.

$[10]$

b$)$ Models $M_1$ and $M_2$ are available smartphones to consumers. Each one can be of either good or low quality. There is only one test $T_1$ that can be used. $T_1$ on $M_1$ costs R$100.$ On $M_2,T_1$ costs R$50.$ The cost of repairing an $M_1$ if it is of poor quality is $R700.$ If $M_2$ is of poor quality, the repair costs R$740.$ Test $T_1$ on $M_1$ will confirm good quality with a probability of $0\mathrm{.}8$ and bad quality with a probability of $0\mathrm{.}65.$ Test $T_1$ on $M_2$ will confirm good quality with a probability of $0\mathrm{.}75$ and bad quality with a probability of $0\mathrm{.}7.$ A consumer wants to buy one of the two smartphone models and wants both examined to determine which model is more economic. Construct a decision tree for this problem.

$[10]$

QUESTION TWO

a$)$ Given the following information, draw a Bayesian network.

$[10]$

i$.$ H is only directly influenced by D$.$ Hence H is conditionally independent of $L,O$ and B given D $.$

ii$.$ D is only directly influenced by O and B $.$ Hence D is conditionally independent of L given O and B $.$

iii. L is only directly influenced by O $.$ Hence L is conditionally independent of $D,H$ and B given $0.$

iv$.$ O and B are independent.

b$)$ Use the Bayes network you have constructed:

i$.,$ Show that $P(H|B,D,O,L)=P(H|D).$

$[1]$

ii$.$ Show that $P(B|B,L)=P(B)$

$[1]$

c$)$ Outline the operation of the A$*$ Algorithm.

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