4. Let X; be a random variable from a uniform distribution on the interval [0,b]. Thus the lower bound is known but not the upper bound. You observe n many independent and identically dis- tributed X₂'s. n a. What is the expected value of the sample mean X = 1X₁? i=1 b. How could you transform X to make it an unbiased estimator of b (that is to: say of the estimator is equal to b)? the expectation

3. Let Y₁ 5)

Let X1, X2, .. ., Xn be a random sample from a normal distribution with mean u and variance o?. Find an estimator for o? using the method of moments. Is this estimator bi- ased/unbiased? Is it consistent?

Suppose that X has a Weibull distribution with β = 2 and δ = 2400. Determine the following. a. P(X > 5000) = b. For an exponential random variable with the same mean as the Weibull distribution  P(X > 5000) =