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4. Let X denote the number eggs hatched out of Y eggs laid by a particular...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,1,2, ..., k> 1 is an integer, 0 <P1 <1,0 <p2 <1, and p1 + P2 <1, find the marginal pmfs of X and Y and the conditional pmf of Y given X = r.
Please answer all the questions and with the given hint. Thanks 2. An ad hoc committee...
Please answer all the questions and with the given hint.
Thanks
2. An ad hoc committee of three is selected randomly from a pool of 10 students consisting of 3 seniors, 3 juniors, 2 sophomores and 2 freshmen students. Let X be the number of seniors and Y be the number of juniors selected. The joint pmf of (X,Y) is, (*)(3)(3-6-v. px,y(x,y) = \* -2-y!, for x = 0,1,2,3, and y = 0,1,2,3 such that I +y < 3 =...
2. Let the random variables X and Y have the joint PDF given below: (a) Find P(X + Y ≤ 2). (b) Find the marginal PDFs o...
2. Let the random variables X and Y have the joint PDF given
below:
(a) Find P(X + Y ≤ 2).
(b) Find the marginal PDFs of X and Y.
(c) Find the conditional PDF of Y |X = x.
(d) Find P(Y < 3|X = 1).
Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
I just need the second problem done. Problem #2 refers to the problem #1. Problem # 1. Let discrete random variables X...
I just need the second problem done. Problem #2 refers to the
problem #1.
Problem # 1. Let discrete random variables X and Y have joint PMF cy 2,0,2 y=1,0, 1 otherwise = Px.y (x, y) 0 Find: a) Constant c X], P[Y <X], P[X < 1 b) P[Y 2. Let X and Y be the same as in Problem # 1. Find: Problem a) Marginal PMFs Px() and Py(y) b) Expected values E[X] and E[Y] c) Standard deviations ox...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of t...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of trials up to and including the first success and let Y denote the number of trials up to and including the second success. a) Identify the (marginal) PMF of X c) Determine the joint PMF of X and Y. d) Use Proposition 6.2 on page 263 and the result of part (c) to obtain the marginal PMFS of X and Y....
3. Let X denote the temperature (°C) and let Y denote the time in minutes that...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
1) Let random variables X and Y have the joint PMF: otherwise a) Calculate the value...
1) Let random variables X and Y have the joint PMF: otherwise a) Calculate the value of c b) Specify the marginal PMFs Pr(x) and P- c) Calculate P[X +Y<0].
Let X denote the number of times a photocopy machine will malfunction: 0,1,2, or 3 times,...
Let X denote the number of times a photocopy machine will malfunction: 0,1,2, or 3 times, on any given month. Let Y denote the number of times a technician is called onan emergency call. The joint p.m.f. p(x,y) is presented in the table below: y\. 0 1 2 3 0 0.15 0.30 0.05 0 1 0.05 0.15 0.05 0.05 2 0 0.05 0.10 0.05 Px(2) 0.20 0.50 0.20 0.10 py(y) 0.50 0.30 0.20 1.00 (a) Find the probability distribution of...
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27...
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,1,2, ..., k> 1 is an integer, 0 <P1 <1,0 <p2 <1, and p1 + P2 <1, find the marginal pmfs of X and Y and the conditional pmf of Y given X = r.
Please answer all the questions and with the given hint.
Thanks
2. An ad hoc committee of three is selected randomly from a pool of 10 students consisting of 3 seniors, 3 juniors, 2 sophomores and 2 freshmen students. Let X be the number of seniors and Y be the number of juniors selected. The joint pmf of (X,Y) is, (*)(3)(3-6-v. px,y(x,y) = \* -2-y!, for x = 0,1,2,3, and y = 0,1,2,3 such that I +y < 3 =...
2. Let the random variables X and Y have the joint PDF given
below:
(a) Find P(X + Y ≤ 2).
(b) Find the marginal PDFs of X and Y.
(c) Find the conditional PDF of Y |X = x.
(d) Find P(Y < 3|X = 1).
Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
I just need the second problem done. Problem #2 refers to the
problem #1.
Problem # 1. Let discrete random variables X and Y have joint PMF cy 2,0,2 y=1,0, 1 otherwise = Px.y (x, y) 0 Find: a) Constant c X], P[Y <X], P[X < 1 b) P[Y 2. Let X and Y be the same as in Problem # 1. Find: Problem a) Marginal PMFs Px() and Py(y) b) Expected values E[X] and E[Y] c) Standard deviations ox...
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of trials up to and including the first success and let Y denote the number of trials up to and including the second success. a) Identify the (marginal) PMF of X c) Determine the joint PMF of X and Y. d) Use Proposition 6.2 on page 263 and the result of part (c) to obtain the marginal PMFS of X and Y....
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
1) Let random variables X and Y have the joint PMF: otherwise a) Calculate the value of c b) Specify the marginal PMFs Pr(x) and P- c) Calculate P[X +Y<0].
Let X denote the number of times a photocopy machine will malfunction: 0,1,2, or 3 times, on any given month. Let Y denote the number of times a technician is called onan emergency call. The joint p.m.f. p(x,y) is presented in the table below: y\. 0 1 2 3 0 0.15 0.30 0.05 0 1 0.05 0.15 0.05 0.05 2 0 0.05 0.10 0.05 Px(2) 0.20 0.50 0.20 0.10 py(y) 0.50 0.30 0.20 1.00 (a) Find the probability distribution of...
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
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