Please provide the workings for the questions below. Thank you

6107 PM Thu 2 Sep 2 EX. 3.50. Suppose that X and Y have the following joint probability distribution: \"324 1 0.10 0.15 3 0.20 0.30 5 0.10 0.15 Values of ag, 3;). (a) Find the marginal distribution of X. (b) Find the marginal distribution of Y. CU Ex. 3.52. A coin is tossed twice. Let Z denote the number of heads on the rst toss and W, the total number of heads in the 2 tosses. If the coin is unbalanced and a head has a 30% chance of occurring, nd (a) the joint probability distribution of W and Z; (b) the marginal distribution of W; (c) the marginal distribution of Z; (d) the probability that a least 1 head occurs. [Answerz (d) 0.5 1.] Ex. 3.56. The joint probability density function of the random variables X and Y is 1 6m, 0 0.3|Y : 0.5). [Answer: (13) 0.64.] Ex. 3.66. Consider the following joint probability density function of the random variables X and Y: 1 9H3}. 05mLOSySL f(sc,y) _ { 0, elsewhere. [Answerz (b) 0.515625] (a) Find the marginal distribution of X and Y. (b) Find P(X > 0.25,Y > 0.5). Ex. 3.76. Let X1 and X2 be random variables having a joint distribution given by i 63:2,0