A Bayesian network is represented in the graph below with each variable to be binary. There are 8 observations as listed in the t below. Now please estimate P(A=1) and P(E=1|B=1,C=1). A A 1 0 1 1 0 B 0 0 1 1 1 D B F E C D E F 1 0 1 1 1 1 0 1 1 1 01 0 0 0 0 1 0 1 0 00 0 1 1 0 01 1 0 1 1 0 1 0 0 0 0 C

Consider the traffic flow described by the following diagram. The letters A through D label intersections. The data was obtained by counting the number of vehicles that travelled around the four one-way streets between the hours of 6 am to 10 am, and 2 pm to 6 pm during the mid-week peak traffic hours. The arrows in the diagram indicate the direction of flow of traffic in and out of the network that is measured in terms of number of vehicles per hour (vph). 3a) Write the system of linear equations for each intersection. 3b) Use Gauss-Jordan elimination to solve the system.

Suppose two variables A and B are correlated. Increase or Decrease a.) If A and B are positively correlated, as A increases in value, B will     .b.) If A and B are negatively correlated, as A increases in value, B will     .c.) If A and B are positively correlated, as A decreases in value, B will     .d.) If A and B are negatively correlated, as A decreases in value, B will     .

Claim: A majority of adults would erase all of their personal information online if they could. A software firm survey of 636 randomly selected adults showed that 58​% of them would erase all of their personal information online if they could. Complete parts​ (a) and​ (b) below. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.