Need solution to all questions. There is another question that could not fit into the screenshot. Will share in comments later

6. A condence interval for uniform distributions I Bookmarked {a} 2 points possible {graded} Let X1, , X" be i.i.d. uniform random variables in [0,6], for some a > I]. Denote by M": :LHFHXH}. Compute the following probabilities: P(an'll= Forallostsm Hungr): [Foodfor thought: What can you conclude?) RD NO ATIDN SLsmit You have used 0 of3 attempts Save {b} 2 points possible (graded:- Compute the cumulaljve distribution function Fun) of "(l Mum} for xed t E [um] and any positive integer n. Fn m = Compute the following limit mnvo U} = [Foodforrhought' Again. What can you conclude?) STAN DARD NO ATI D N Span-lit You have used 0 of3 attempts Save it} 2 points possible (graded:- Next. we will use the previous question to nd an interval 1 of the form I = [Me Mn+ c] , that does not depend on a and such that FUSE] u .95, also > oo. The strategy now is to use a plug-in estimator for a to replace it in the expression for c. Pans {a} and (b) suggest that we use c of the form (i) M" where r ought to equal a certain value in order for 1' [I a 8'] .95. What is [he appropriate numerical value of r? r = Why can we use a pluginesljmator for the asymptotic condence interval? VB): the Delta Method, the asymptotic variance scales with the square of the first derivative of the plugin function. uBy Slutsky's Theorem, we can combine convergence in distribution of Y" and in probability of 2,, if 2,; converges to a constant. Q-By the Central Limit Theorem. the plugin variable will again be normally distributed