Question: If X lnY has a normal distribution with the
If X = lnY has a normal distribution with the mean µ and the standard deviation s, find the probability density of Y which is said to have the log– normal distribution.
Answer to relevant QuestionsWith reference to the two random variables of Exercise 7.5, show that if θ1 = θ2 = 1, the random variable Z = X1/X1 + X2 has the uniform density with α = 0 and β = 1. Exercise 7.5 If X1 and X2 are independent random ...Use the condition of Exercise 8.9 to show that the central limit theorem holds for the sequence of random variables of Exercise 8.8. In exercise Show that the formula for the sample variance can be written as Also, use this formula to recalculate the variance of the sample data of Exercise 8.18. Use the method of Exercise 8.25 to find the approximate value of the probability that a random variable having a chi-square distribution with v = 50 will take on a value greater than 68.0. If X1, X2, . . . , Xn are independent random variables having identical Bernoulli distributions with the parameter θ, then is the proportion of successes in n trials, which we denote by Θ. Verify that (a) E(Θ) = θ; ...
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