London

is the management accountant at Norse

Credit. Norse

Credit spends a lot of time and resources trying to detect fraudulent activity within$$ customers' accounts. For most customers this is a low probability event.$$ However, if it happens and Norse

Credit does not detect$$ it$,$ it is very costly for the company. London

is working with the data science team to improve models for predicting fraudulent activity in$$ customers' accounts. The table below lists six observations in a$$ model's validation sample and the probability of default predicted by the$($pruned$)$ decision tree.

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Question content area bottom

Part $1$

Requirement $1.$ Calculate the likelihood value for each observation in the validation set using the following equation L$=$ py

$\backslash$times $(1$

$-$p$)1$

$-$ y$($remember: x$$

$=$ x and x$$

$=1).($Enter the likelihood values to two decimal$$ places, X$.$XX$.)$

Actual Outcome

Probability of Fraud Predicted by the Pruned Decision Tree

Likelihood Value

Observation

$($y$)$

$($p$)$

$*$

$(1)$

$(2)$

$(3)$

$(4)$

$1$

$1($fraud$)$

$0\mathrm{.}45$

$0\mathrm{.}45$

$2$

$0($clean$)$

$0\mathrm{.}30$

$0\mathrm{.}70$

$3$

$0($clean$)$

$0\mathrm{.}01$

$0\mathrm{.}99$

$4$

$0($clean$)$

$0\mathrm{.}99$

$0\mathrm{.}01$

$5$

$0($clean$)$

$0\mathrm{.}70$

$0\mathrm{.}30$

$6$

$0($clean$)$

$0\mathrm{.}01$

$0\mathrm{.}99$

$*$py

$\backslash$times $(1-$p$)1$

$-$ y

Part $2$

Requirement $2.$ Calculate the overall likelihood value for this set of predictions by multiplying the likelihood values for each observation together. $($Enter the overall likelihood to five decimal$$ places, X$.$XXXXX$.)$

Overall Likelihood Value $=$