The joint distribution of X and Y is given by: 3x²-2y f(x,y) = For x = -1,0,2 and y = -1,0. Then k = O 36 O 24 O 18 ) None of these
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- part d,e,fQ1,Q2* 6) A triangular distribution has p.d.f.) f(x)= k(1- Sketch the p.d.f., and evaluate the constant k. (xl) for 1The magnitudes of Earthquake and Tsunami are given by the variables of m and n, respectively. Their joint occurrence probability is given by the joint probability mass function as: f (m, n) = A (m2 + n?) for the magnitudes of zero, one, two and three. a) Find the value of the constant A. b) Find the mean value of the joint occurrence function of these magnitudes. c) Determine the marginal distributions of these magnitudes. d) If an earthquake of magnitude 1 occurred, find the probability of having a tsunami of magnitude 2 and greater. e) Determine if the magnitude of earthquake and tsunami are independent random variables. Prove your opinion.The time (in minutes) it takes Greg to complete a homework problem is uniformly distributed (continuously) on the interval (15, 28). What is the standard deviation of the time it takes to complete a homework problem?I need the answer quickly please3x-2y For x =-1,0,1 and y = -1,0. The joint distribution of X and Y is given by: f(x.y) = For x = -1,0,1 and y = -1,0. Then k = None of these O 18 24 36number 24 onlyIt is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 50 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 153, Σx2 = 65, Σy2 = 6201, Σxy = 409, and r ≈ −0.991 (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r =