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Probability from a Joint Probability Distribution Function

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Five independent observations are drawn from the pdf, f(t) = 2t, 0<=t<=1. X is a random variable that denotes the number of t's that fall in the interval 0<=t<1/3. Y is a random variable that denotes the number of t's that lie in the interval 1/3<=t<2/3. Find p(x,y)=p(1,2).

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A step-by-step solution is provided. The detailed solution shows how to take a joint pdf and calculate a probability. A simple example using a continuous pdf illustrates the process.

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The key to solving this problem is to recall the formula for p(x,y). In our example, we have 5 independent trials, each ending in one of three possible outcomes. The three outcomes are that any given t can ...

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