Let there be U, a random variable that is uniformly distributed over [0,1] . Find: 1)...

Question

Question

Let there be U, a random variable that is uniformly distributed over [0,1] $U Uni0,1$ . Find:

1) Density function of the random variable Y=min{U,1-U}. How is Y distributed?

2) Density function of 2Y

3)E(Y) and Var(Y)

Answer 1

Answer #1

Drawing the graph and finding the cdf of the rv makes it easier to solve the problem.

The second problem is solved by the process of transformation of variable hence by calculating jacobian.

Third problem is simple expectation and variance calculation. UU(oi) 2-

2. 2. v/1-1) = 12 12 12 3 = 12.

Answer 2

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