Breaking stuff let {xi} n i=1 be a sample of random variables of size n with the property that xi ∼ n (µ, σ2 ) and cov(xi , xj ) = ρσ for all pairs i, j. a. solve for the mean and variance of x¯. b. what happens to the variance of x¯ as n → ∞? c. why do the clt and lln fail in this situation? d. using the provided code, simulate s = 1000 values of x¯ for n = 50, 100, 500. in all three cases calculate the mean and variance of the resulting distribution. create histograms for each. in this code, σ = 1 and ρ = .4. how does the variance for each n compare to the formula from part (a)?

() (98 points)to be fair, you have to have a very high iq to understant the jokes in rick and morty. the humour is extremely subtle, and without a solid grasp of theoretical physics most of the jokes will go over a typical viewer's head. there's also rick's nihilistic outlook, which is deftly woven into his characterisation- his personal philosophy draws heavily from narodnaya volya literature, for instance. the fans understand this stuff; they have the intellectual capacity to truly appreciate the depths of these jokes, to realise that they're not just funny- they say something deep about life. as a consequence people who dislike rick & morty truly are idiots- of course they wouldn't appreciate, for instance, the humour in rick's existential catchphrase "wubba lubba dub dub," which itself is a cryptic reference to turgenev's russian epic fathers and sons. i'm smirking right now just imagining one of those addlepated simpletons scratching their heads in confusion as dan harmon's genius wit unfolds itself on their television screens. what fools.. how i pity them. and yes, by the way, i do have a rick & morty tattoo. and no, you cannot see it. it's for the ladies' eyes only- and even then they have to demonstrate that they're within 5 iq points of my own (preferably lower) beforehand. nothin personnel kid

How many lines can be drawn through points j and k? 0 1 2 3

Adrawer contains 12 identical white socks, 18 identical black socks and 14 identical brown socks. what is the least number of socks you must choose, without looking, to be certain that you have chosen two socks of the same colour?