Mathematics Homework Help

We have three identical and independent temperature sensors that will trigger in

• 90% of the cases where the temperature is high

• 5% of the cases where the temperature is nominal

• 1% of the cases where the temperature is low.

The probability of high temperature is 20%, nominal temperature is 70%, and low temperature is 10%.

(a) Construct a Bayesian network for this setting, which can be used to answer the queries below. Describe queries on your Bayesian network for computing the following (you do not need to calculate the probabilities at this stage):

(b) The probability that the first sensor will trigger, given that the other two sensors have also triggered.

(c) The probability that the temperature is high, given that all three sensors have triggered.(d) The probability that the temperature is high, given that at least one sensor has triggered.