3. Three different roads feed into a particular freeway entrance. Suppose that d

Question

3. Three different roads feed into a particular freeway entrance. Suppose that during a fixed period, the number of cars coming from each road on the freeway is a random variables, with expected value and standard deviation as given in the following table. Expected Value Standard Deviation Road 1 800 16 Road 2 1000 25 Road 3 600 18 (a) What is the expected total number of cars entering the freeway through this entrance during the fixed period? b) What is the variance for the total number of cars entering the freeway through this entrance during the fixed period? Assume that the number of cars from each road are independent of each other.

Explanation / Answer

a) total number of cars =E(R1)+E(R2)+E(R3) =800+1000+600 =2400

b)std deviation =(Var(R1)+Var(R2)+Var(R3))1/2 =(162+252+182)1/2 =34.7131

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