A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going...

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Extracted text: A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let X1 denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by X2 X1 1 2 3 4 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 0.03 0.11 0.15 0.01 0.01 0.02 0.07 0.10 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of X1 given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give E(X1| X2=3). (g) Give the standard deviation of X1.