Independent Random Probability Assignment | Homework For You
Consider two independent random samples of size 10 and 20 from normal populations: ð‘‹!, ð‘‹!,…, ð‘‹!” ~ ð‘›ð‘œð‘Ÿð‘šð‘Žð‘™ ðœ‡! = 12.2, ðœŽ! = 2.2 ð‘Œ!, ð‘Œ!,…, ð‘Œ!” ~ ð‘›ð‘œð‘Ÿð‘šð‘Žð‘™ ðœ‡! = 12.6, ðœŽ! = 2.2 (a) Find the probability that the sample variance ð‘†! ! is more than twice its population value, ðœŽ! !. Is it the same as the probability that ð‘†! ! is more than twice its population value, ðœŽ! !? 
Explain why is this what you would expect. [3] (b) Find the probability that ð‘†! ! is more than twice ð‘†! !. Is it the same as the probability that ð‘†! ! is more than twice ð‘†! !? [Hint: what is the distribution of ð‘†! ! ð‘†! !?] [3] (c) A random sample of ð‘› = 30 values from a different normal distribution with unknown parameters 𜇠and ðœŽ! has sample mean and standard deviation ð‘¥ = 17.2 and ð‘ = 3.1 Find 95% confidence intervals for 𜇠and ðœŽ. Get Statistics homework help today
