# Question

If the range of X is the set of all positive real numbers, show that for k > 0 the probability that √2X – √2v will take on a value less than k equals the probability that X – v / √2v will take on a value less than k + k2 / 2√2v.

## Answer to relevant Questions

Use the results of Exercises 8.25 and 8.27 to show that if X has a chi-square distribution with v degrees of freedom, then for large v the distribution of √2X – √2v can be approximated with the standard normal ...Show that for v2 > 2 the mean of the F distribution is v2 / v2 – 2, making use of the definition of F in Theorem 8.14 and the fact that for a random variable V having the chi-square distribution with v2 degrees of freedom, ...Show that the F distribution with 4 and 4 degrees of freedom is given by And use this density to find the probability that for independent random samples of size n = 5 from normal populations with the same variance, S21 / ...Find the sampling distribution of Y1 for random samples of size n = 2 taken (a) Without replacement from the finite population that consists of the first five positive integers; (b) With replacement from the same ...Looking at binomial random variables as on page 226, that is, as sums of identically distributed independent Bernoulli random variables, and using the central limit theorem, prove Theorem 6.8 on page 191.Post your question

0