1. 0 and 1? Really? U is [0,1], then 1-U is on [1,0], then 29(1-U) is on [29,0], and finally 29(1-U)-(1/5) is on [29 - 1/5, 0 - 1/5]
Of course, you probably didn't mean what you wrote.
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.