Please complete the following problem correctly, showing all steps in computation:
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Please complete the following problem correctly, showing all steps in computation: Part 4 Two random variables...
Please complete the following problem correctly, showing all steps in computation: B. We have two random...
Please complete the following problem correctly, showing all
steps in computation:
B. We have two random variables T and Q, both are discrete variables. Sample space of T is 11, 2, 3} and sample space of Q is {10, 20} The joint distribution is shown as follows Calculate the Covariance of T and Q. (25 points) 10 20 0.4 0.05 2 0.1 0.1 0.05 0.3
2. Let X and X be two random variables with the following joint PMF Yix 2...
2. Let X and X be two random variables with the following joint PMF Yix 2 0 2 0 0.1 0.05 0.05 0.15 0.1 0.05 0.1 0.05 0.05 0.05 4 0.05 0.05 0.02 0.1 0.03 total 0.2 0.2 0.12 0.3 0.18 total 0.45 0.3 0.25 1 1) Find E[X] and E[Y]. (10 points) 2) What is the covariance of X and Y? (20 points) 3) Are X and Y independent? Explain. (10 points)
1 * Consider the following joint distribution for the weather in two consecutive days. Let X...
1 * Consider the following joint distribution for the weather in two consecutive days. Let X and Y be the random variables for the weather in the first and the second days, whereas the weather is coded as 0 for sunny, 1 for cloudy, and 2 for rainy. 0 0.2 0.2 0.2 10.1 0.1 0.1 2 0 0.1 0 (a) Find the marginal probability mass functions for X and Y (b) Are the weather in two consecutive days independent? (c)...
1. The joint PDF of two random variables are given in the following table a) (0.3...
1. The joint PDF of two random variables are given in the following table a) (0.3 points) Are X and Y independent? Explain. b) (0.3 point) Find E(X) c) (0.3 points) Find E(Y) d) (0.4 points) Find E(max(X, Y)) e) (0.4 points) Calculate P(X Y). ) (0.5 points) Calculate covariance of X and Y g) (0.5 points) Calculate correlation coefficient of X and Y 0 0.32 0.48 10.080.12
Please complete the following problem correctly, showing all steps and work: B. Use the properties of...
Please complete the following problem correctly, showing all
steps and work:
B. Use the properties of expected value and variance, show If X is a random variable with mean μ and variance σ, then Y--μ has mean 0 and variance o2. (7.5 points) a. b. If X mean 0 and variance 1. (7.5 points) is a random variable with mean μ and variance σ. the n Z = (X-μ)/σ has
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random vari...
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
please write step by step and clear extend answer (d) Consider two random variables X and...
please write step by step and clear extend answer
(d) Consider two random variables X and Y. They both take the values -1,0 and 1. The joint probabilities for each pair are given by the following table: Y = -1 Y=0 Y = 1 X = -1 X = 0 X = 1 0.2 0.05 0.15 0.1 0.1 0.1 0.1 0.05 0.15 i. Calculate P(Y = 1). ii. Calculate P(Y = 0 X + Y = 0). (2 marks) (4...
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete...
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete random variables defined on the same sample space. Then X and Y are independent if and only if pxy(x,y) = px(x)py(y), for all x , y ER. (6.19) In words, two discrete random variables are independent if and only if their joint equals the product of their marginal PMFs. Proposition 6.11 Independence and Conditional Distributions Discrete random variables X and Y are independent if and only...
Please answer the following statistics problem and show all your steps thoroughly! Thank you! Question...
Please answer the following statistics problem and show
all your steps thoroughly! Thank you!
Question 5 (10 marks) Suppose that (X, Y) have joint probability function f(x,y) specified by the following table: f(x,y) 0 0.2 0.15 1 Х 2 0.3 0 1 0.1 0.1 3 0.05 0.1 у 2 a) (2 marks) Find the marginal distribution of X and Y (display in a table) b) (2 marks) Find the conditional distribution of Y given X=3. (display in a table)...
Suppose that the following table is the joint probability distribution of two random variables X and...
Suppose that the following table is the joint probability distribution of two random variables X and Y: х -2 0 2 3 0.27 0.08 0.16 0.2 0.1 0.04 0.1 0.05 a. Find the marginal PDF of X when x=-2, 0, 2, and 3. b. Find the marginal PDF of Y when y=2 and 5. . Find the conditional PDF of x=-2 and 3 given that y=2 has occurred. . Find the conditional PDF of y=2 and 5 given that x=3...
Please complete the following problem correctly, showing all
steps in computation:
B. We have two random variables T and Q, both are discrete variables. Sample space of T is 11, 2, 3} and sample space of Q is {10, 20} The joint distribution is shown as follows Calculate the Covariance of T and Q. (25 points) 10 20 0.4 0.05 2 0.1 0.1 0.05 0.3
2. Let X and X be two random variables with the following joint PMF Yix 2 0 2 0 0.1 0.05 0.05 0.15 0.1 0.05 0.1 0.05 0.05 0.05 4 0.05 0.05 0.02 0.1 0.03 total 0.2 0.2 0.12 0.3 0.18 total 0.45 0.3 0.25 1 1) Find E[X] and E[Y]. (10 points) 2) What is the covariance of X and Y? (20 points) 3) Are X and Y independent? Explain. (10 points)
1 * Consider the following joint distribution for the weather in two consecutive days. Let X and Y be the random variables for the weather in the first and the second days, whereas the weather is coded as 0 for sunny, 1 for cloudy, and 2 for rainy. 0 0.2 0.2 0.2 10.1 0.1 0.1 2 0 0.1 0 (a) Find the marginal probability mass functions for X and Y (b) Are the weather in two consecutive days independent? (c)...
1. The joint PDF of two random variables are given in the following table a) (0.3 points) Are X and Y independent? Explain. b) (0.3 point) Find E(X) c) (0.3 points) Find E(Y) d) (0.4 points) Find E(max(X, Y)) e) (0.4 points) Calculate P(X Y). ) (0.5 points) Calculate covariance of X and Y g) (0.5 points) Calculate correlation coefficient of X and Y 0 0.32 0.48 10.080.12
Please complete the following problem correctly, showing all
steps and work:
B. Use the properties of expected value and variance, show If X is a random variable with mean μ and variance σ, then Y--μ has mean 0 and variance o2. (7.5 points) a. b. If X mean 0 and variance 1. (7.5 points) is a random variable with mean μ and variance σ. the n Z = (X-μ)/σ has
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
please write step by step and clear extend answer
(d) Consider two random variables X and Y. They both take the values -1,0 and 1. The joint probabilities for each pair are given by the following table: Y = -1 Y=0 Y = 1 X = -1 X = 0 X = 1 0.2 0.05 0.15 0.1 0.1 0.1 0.1 0.05 0.15 i. Calculate P(Y = 1). ii. Calculate P(Y = 0 X + Y = 0). (2 marks) (4...
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete random variables defined on the same sample space. Then X and Y are independent if and only if pxy(x,y) = px(x)py(y), for all x , y ER. (6.19) In words, two discrete random variables are independent if and only if their joint equals the product of their marginal PMFs. Proposition 6.11 Independence and Conditional Distributions Discrete random variables X and Y are independent if and only...
Please answer the following statistics problem and show
all your steps thoroughly! Thank you!
Question 5 (10 marks) Suppose that (X, Y) have joint probability function f(x,y) specified by the following table: f(x,y) 0 0.2 0.15 1 Х 2 0.3 0 1 0.1 0.1 3 0.05 0.1 у 2 a) (2 marks) Find the marginal distribution of X and Y (display in a table) b) (2 marks) Find the conditional distribution of Y given X=3. (display in a table)...
Suppose that the following table is the joint probability distribution of two random variables X and Y: х -2 0 2 3 0.27 0.08 0.16 0.2 0.1 0.04 0.1 0.05 a. Find the marginal PDF of X when x=-2, 0, 2, and 3. b. Find the marginal PDF of Y when y=2 and 5. . Find the conditional PDF of x=-2 and 3 given that y=2 has occurred. . Find the conditional PDF of y=2 and 5 given that x=3...
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