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    I've been stuck for a while on this part. Help would be really appreciated!

    Let X1, . . . , Xn be IID Exponential(?) random variables. Use mgfs to find the distributionofY =X1 +...Xn.
  2. A

    Joint density. Help!

    Let x and y have the joint density: f(x,y) = 6/7(x+y)^2 for 0<=x<=1 and 0<=y<=1 a.Find the marginal densities of X and Y. . b.By integrating over the appropriate regions, find: i)P(X>Y) ii)P(X+Y)<=1 iii)P(x>=1/2) For this one, I got the answer for part(i). That is 1-P(X<=Y). but...
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    Independence of Bivariate Continuos RV's.

    By the two definitions of independence for bivariate continuous RVs: (1) F(x,y)=F_X(x)F_Y(y) and (2) f(x,y)=f_X(x)f_Y(y). Prove that these two are equivalent. That is: prove that (1) implies (2) and that (2) implies (1). I tried to differentiate for one and integrate for the other.
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    Functions of Random Variable.

    Let X be exponential(lambda), and let Y=max(1,X). Find the cdf of Y. Also sketch the cdf. Suppose that X is discrete with pmf p(0)=p(1)=2p(2) (and zero otherwise). Find the pmf and cdf of X. How would you simulate the random variable X starting with U, a uniform[0,1] random variable? That is...
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    Joint and Marginal Densities.

    I am having some problems grasping the concept of these joint and marginal densities. It would really help if someone could provide me with an answer for the following question: Find the joint and marginal densities corresponding to the cdf F(X, Y) = (1 - е^αx){1-e^βy), x > 0, y>0, α >...