# Question: Find the joint probability density of the two random variables

Find the joint probability density of the two random variables X and Y whose joint distribution function is given by

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Use the joint probability density obtained in Exercise 3.54 to find P(1< X ≤ 2, 1< Y ≤ 2). In exercise Use the formula obtained in Exercise 3.58 to verify the result of Exercise 3.57. In exercise If F(x, y) is the value of the joint distribution function of the two continuous random variables X and Y at (x, y), express P(a < ...With reference to Exercise 3.42 on page 90, In exercise If the values of the joint probability distribution of X and Y are as shown in the table Find (a) The marginal distribution of X; (b) The marginal distribution of Y; ...With reference to Example 3.22 on page 94, In exercise The p. d. f. of the random variable X is given by Find (a) The conditional density of X2 given X1 = 1/3 and X3 = 2; (b) The joint conditional density of X2 and X3 ...With reference to Exercise 3.80 on page 101, find the distribution function of the sum of the spots on the dice, that is, the probability that this sum of the spots on the dice will be at most S, where S = 2, 3, . . . , 12.Post your question