Consider the generation of two random numbers between 0 and 1. If X represents their sum,...

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Consider the generation of two random numbers between 0 and 1. If X represents their sum, then it can take on any value between 0 and 2. The density curve of X is the triangle shown below. 0 1 2 Height = 1 (a) Verify that this is a density curve (which 2 conditions do we need?) (b) What is the probability that X is less than 1? [Sketch the density curve, shade the area that represents the probability, then find that area. This can be done by hand. Do this for part (c) also.] (c) What is the probability that X is less than 0.85? Hint: Which area do we need? Consider the generation of two random numbers between 0 and 1. If X represents their sum, then it can take on any value between 0 and 2. The density curve of X is the triangle shown below. 0 1 2 Height = 1 (a) Verify that this is a density curve (which 2 conditions do we need?) (b) What is the probability that X is less than 1? [Sketch the density curve, shade the area that represents the probability, then find that area. This can be done by hand. Do this for part (c) also.] (c) What is the probability that X is less than 0.85? Hint: Which area do we need?

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