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Probabilities and Networks

Calculate the following probabilities for a patient who is about to undergo CABG (coronary artery bypass graft) surgery:

? The only possible, mutually exclusive outcomes of the surgery are death, relief of symptoms, or continuation of symptoms. The probability of death is 0.02 and the relief of symptoms is 0.80. What is the probability that the patient will continue to have symptoms? To get full credit, show calculation work for your answer

? Two known complications of heart surgery are stroke and heart attack, with a probability of 0.02 and 0.05, respectively. The patient asks what chances he has of having both complications. Assume that the complications are conditionally independent. To get full credit, show calculation work for your answer

? The patient wants to know the probability that he will have a stroke given that he has a heart attack as a complication of surgery. For your calculation, assume that 1 in 500 patients have both complications, that the probability of heart attack is 0.05, and that the events are independent. To get full credit, show calculation work for your answer

Question 2. Calculate the output of the network given the following neural network:

Weights between input and hidden layer are as follows:

w11 = 1.2 w12 = 1.5 w21 = 1.5 w22 = 2.0 w31 = 2.0 w32 = 1.0

Weights between input and hidden layer are as follows:

w11 = 1.5 w21 = 2.1

Inputs are:

x1 = 0.7 x2 = 0.9 x3 = 0.1

Assume that the transfer function of the input and hidden layers as linear and bias of 1 and that of output neuron as sigmoid function, of the form:

y = , where x = input, y is output, and i = bias

Begin by mapping the aforementioned information, as done for you below:

Step 1: Calculate the weighted sum coming into h1, as done below:

h1 = (x1 * 1.2) + (x2 * 1.5) + (x3 * 2.0)

h1 = (0.7 * 1.2) + (0.9 * 1.5) + (0 .1 * 2.0)

h1 = 0.84 + 1.35 + 0.2

h1 = 2.39

Step 2: Apply the sigma function to h1, as done below:

y = = = = = 0.92

Step 3: Calculate the weighted sum coming into h2,Show calculations

Step 4: Apply the sigma function to h2,Show calculations

Step 5: Calculate the weighted sum going into y,Show calculations

Step 6: Apply the sigmoid output from the network for y,Show calculations

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