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Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ. Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the P...
Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2), respectively. (a) Find the...
Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2),
respectively.
(a) Find the distribution of Z = X + Y .
(b) Find the distribution of X|X + Y .
(c)If X∼Pois(λ1) and Y|X=x∼Bin(x,p). Find the distribution of
Y.
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z= X+Y. (b) Find the distribution of X|X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p)....
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the...
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X X +Y. (c) If X Pois(11) and Y|X = r ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of...
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X +Y. (b) Find the distribution of X X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(11) and Pois(2), respectively....
2. (30 pts) Let X and Y be independent rv's with pmf Pois(11) and Pois(2), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X+Y. (c) If X Pois (41) and Y|X = x~ Bin(x, p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively....
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X +Y.. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find...
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
Let X be a Poisson (mean = 5) and Let Y be a Poisson (mean = 4). Let Z = X + Y. Find P( X = 3 | Z = 6). Assume X and Y are independent. Show answers for P(A), P(B), P(AB), and and hence P(A|B). Here...
Let X be a Poisson (mean = 5) and Let Y be a Poisson (mean = 4). Let Z = X + Y. Find P( X = 3 | Z = 6). Assume X and Y are independent. Show answers for P(A), P(B), P(AB), and and hence P(A|B). Here A = [X = 3], B = [Z = 6]
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label)...
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label) of the first success observed, and Y be the location of the second success observed. (a) Find the joint PMF of X and Y; give your result as a general formula. (It may help to start by considering specific sequences, such as "001001", where X 3 and 6 (b) Write out thefirst of your PMF in table format, covering the range 1 sX 4,13YS...
Let the joint pmf of X and Y be defined by x+y 32 x 1,2, y,2,3,4...
Let the joint pmf of X and Y be defined by x+y 32 x 1,2, y,2,3,4 (a) Find fx(x), the marginal pmf of X. b) Find fyv), the marginal pmf of Y (c) Find P(XsY. (d) Find P(Y 2x). (e) Find P(X+ Y 3) (f) Find PX s3-Y) (g) Are Xand Y independent or dependent?Why or why not? (h) Find the means and the variances of X and Y
and Y ~ Geometric - 4 Let X ~ Geometric We assume that the random variables X and Y are statistically independent. Answer the following questions: a (3 marks) For all x E 10,1,2,...^, show that 2+1 P...
and Y ~ Geometric - 4 Let X ~ Geometric We assume that the random variables X and Y are statistically independent. Answer the following questions: a (3 marks) For all x E 10,1,2,...^, show that 2+1 P(X>x) P(x (3 = Similarly, for all y [0,1,2,...^, show that Show your working only for one of the two identities that are pre- sented above. Hint: You may use the following identity without proving it. For any non-negative integer (, we have:...
Let X and Y be independent rv’s with pmf Pois(λ1) and Pois(λ2),
respectively.
(a) Find the distribution of Z = X + Y .
(b) Find the distribution of X|X + Y .
(c)If X∼Pois(λ1) and Y|X=x∼Bin(x,p). Find the distribution of
Y.
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z= X+Y. (b) Find the distribution of X|X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p)....
Let X and Y be independent rv's with pmf Pois(11) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X X +Y. (c) If X Pois(11) and Y|X = r ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X +Y. (b) Find the distribution of X X +Y. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(11) and Pois(2), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X+Y. (c) If X Pois (41) and Y|X = x~ Bin(x, p). Find the distribution of Y.
2. (30 pts) Let X and Y be independent rv's with pmf Pois(41) and Pois(12), respectively. (a) Find the distribution of Z = X+Y. (b) Find the distribution of X|X +Y.. (c) If X ~ Pois(11) and Y|X = x ~ Bin(x,p). Find the distribution of Y.
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
5. A series of independent Bernoulli(p) trials is performed, labeled 1,2,3,...Let X be the location (label) of the first success observed, and Y be the location of the second success observed. (a) Find the joint PMF of X and Y; give your result as a general formula. (It may help to start by considering specific sequences, such as "001001", where X 3 and 6 (b) Write out thefirst of your PMF in table format, covering the range 1 sX 4,13YS...
Let the joint pmf of X and Y be defined by x+y 32 x 1,2, y,2,3,4 (a) Find fx(x), the marginal pmf of X. b) Find fyv), the marginal pmf of Y (c) Find P(XsY. (d) Find P(Y 2x). (e) Find P(X+ Y 3) (f) Find PX s3-Y) (g) Are Xand Y independent or dependent?Why or why not? (h) Find the means and the variances of X and Y
and Y ~ Geometric - 4 Let X ~ Geometric We assume that the random variables X and Y are statistically independent. Answer the following questions: a (3 marks) For all x E 10,1,2,...^, show that 2+1 P(X>x) P(x (3 = Similarly, for all y [0,1,2,...^, show that Show your working only for one of the two identities that are pre- sented above. Hint: You may use the following identity without proving it. For any non-negative integer (, we have:...
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