I'm having troubles with this past paper question. I've touched on ont. Uniform stuff but this is really causing me trouble. Is the first question 0 and 1?
U is a continuous uniform random variable on the range (0, 1). A continuous random variable X is defined by X = 29(1 − U)−1/5.
- Write down the largest and smallest values X can take.
- Use the transformation of random variables technique to calculate the distribution function FX(x) of X.
- Calculate the density function of X and the expectation and variance of X.
- Suppose that X1, X2, ..., X10 are 10 independent copies of X. Use a suitable approximation to calculate the probability that the sample mean of these values is at least as large as 29.
- Comment on the accuracy of the approximation.