Rprogramming:

Suppose we have two separate bags of balls.BagAhasNnumber ofballsinit, some white some black but we don't know how many of each color.BagBhasKwwhiteball(s) and blackball(s).YoudrawRnumberofballsfromBagA and move them to Bag B.Then , you draw T balls sequentially from Bag B.Suppose the sequence ofthetheseballsturnsouttobe[S1;S2;:::;ST].Weareinterestedin the composition of balls in Bag A. List your hypotheses and count up all the ways the observed data can happen. Which hypothesis would you believe more? [30 points] (a) What is the code to calculate the number of ways the observed sequence [S1; S2; : : : ; ST ] canhappenforeachhypothesis.YourfunctionshouldworkforanyvalueofN;Kw;Kb;R ;Tandforanysequenceofballs[S1;S2;:::;ST].[Rcodingonly] [20 points] (b) Which hypothesis is most likely when N = 20; Kw = 10; Kb = 10; R = 5 and the observed sequence is [W; B; B; W; B; W]. [10 points]

3. R programming : Suppose we have twoseparate bags of balls. Bag A has Nnumber of balls in it, some white some black but we don't know how many of each color. Bag Bhas Kw white ball (s) and Kbblack ball(s). Youdraw Rnumber ofballs from Bag A and move them to Bag B. Then , you draw Tballs sequentially from Bag B. Suppose the sequenceofthe these ballsturnsout to be [51, 52,..., Sr]. Weareinterestedin the composition of balls in Bag A. List your hypotheses and count up all the ways theobserved data can happen. Which hypothesis would you believe more? (30 points] (A) Write a code to to calculate the number of ways the observed sequence [Si, $2. ..., Sr] can happen for each hypothesis. Your function should work for any value of N, Kw, Kb, R , Tand for any sequence of balls [$1, 52,..., ST]. [Rcodingonly] 120 points] (b) Which hypothesis is most likely when N = 20, Kw = 10, Kb = 10, R = 5 and the observed sequence is [W. B. B. W. B. W]. [10 points]