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According to Definition 7.1 a random variable X is said to be uniformly distributed over the interval
(a,b) if it has probability density function f(t)={ba10ift(a,b),otherwise. Suppose that 0<a<b. 1.
Determine the probability density function of Y=X+ where >0 and R. 2. Is Y uniformly distributed?
Explain your answer. 3. Determine the expectation of X and Y. 4. Determine the variance of X and
Y.

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  • 1. According to Definition 7.1 a random variable X is said to be uniformly distributed over the interval (a,b) if it has probability density function f(t)={ba10ift(a,b),otherwise. Suppose that 0<a<b. 1. Determine the probability density function of Y=X+ where >0 and R. 2. Is Y uniformly distributed? Explain your answer. 3. Determine the expectation of X and Y. 4. Determine the variance of X and Y.