Artificial Intelligence20765 marksNumerical: Joint probability distributionHandling Uncertain Knowledge, Radom Variables, Prior and Pos
How uncertain knowledge is represented? Given following full joint probability distribution representing probabilities of having different sizes of CD, find the probability that a CD cover has a length of 130mm given the width is 15mm.
How uncertain knowledge is represented? Given following full joint probability distribution representing probabilities of having different sizes of CD, find the probability that a CD cover has a length of 130mm given the width is 15mm.
$$\begin{array}{|c|c|c|c|c|}\hline \text{y=Width} & \text{x=Length} & 129 & 130 & 131 \ \hline 15 & & 0.12 & 0.42 & 0.06 \ 16 & & 0.08 & 0.28 & 0.04 \ \hline \end{array}$$
[5]
Full joint probability distribution: y = Width x = 129 x = 130 x = 131 -------------------------------------- 15 0.12 0.42 0.06 16 0.08 0.28 0.04 Check total: $0.12+0.42+0.06+0.08+0.28+0.04 = 1.00$ ✓ Required: $P(\text{Length}=130 \mid \text{Width}=15)$ --- Real-world AI agents rarely have comple...