Question: 3. (a) Let U be a random variable which follows the uniform distribution U[0, 1] over [0, 1]. Explain why we have E(f (U) )

3. (a) Let U be a random variable which follows the
uniform distribution U[0, 1] over [0, 1]. Explain why we have E(f

3. (a) Let U be a random variable which follows the uniform distribution U[0, 1] over [0, 1]. Explain why we have E(f (U) ) = f(x) dx. (b) Let U:(i = 1, 2, ...,n) be a sequence of random numbers (assuming that U; are independent and follow the uniform distribution U[0, 1]). Explain how one can obtain an approximation (in terms of U;) for the definite integral: sin(x2 ) dx. 0 (10 Points)

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