Please answer the following statistics problem and show all your steps thoroughly! Thank you!
Please answer the following statistics problem and show all your steps thoroughly! Thank you! Question...
Question 1(a&b) Question 3 (a,b,c,d) QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x,...
Please show how did you came up with the answer, show formulas and work. Also, please do Parts e to i. Thank you so much 1. Consider the following probability mass function for the discrete joint probability distribution for random variables X and Y where the possible values for X are 0, 1, 2, and 3; and the possible values for Y are 0, 1, 2, 3, and 4. p(x,y) <0 3 0 4 0.01 0 0 0.10 0.05 0.15...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer. (20 points) Consider the following joint distribution of 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...
Q1. [4+2+4 marks] Consider the following joint probability distribution fxy(x, y). 2 4 0.05 0.1 0,05 0.02 0.1 0.05 2 0.02 0.13 0.3 0.01 0.02 0.15 a) Find the covariance between X and Y b) Are X and Y independent? Explain. c) Find V(X12).
Problem 4 (Conditional Expectation and Variance). Suppose the joint distri- bution of (X, Y) is given by the following contingency (row represents x) table 20 points (x,y) 2 4 6 1 0.3 0 0.1 2 0 0.2 0 3 0.1 0 0.3 A) Compute the marginal distributions of X and Y B) Are X and Y independent? Explain. C) Find the conditional distribution of Y given X -1 D) Compute E[Y|X 1] E) Compute EY|X= 2] F Compute E[exp(X)Y|x 2
. Suppose we have the following joint distribution for random variables X and Y 2 0.1 0.2 0.1 4 0 0.3 0.1 6 0 0 0.2 (a) Find p(X). That is find the marginal distribution of X. (b) Find p(Y). That is find the marginal distribution of Y (c) Find the distribution of X conditional on Y = 3. (d) Find the distribution of X conditional on Y 2 (e) Are X and Y independent? You should be able to...
Question 10 Using the joint probability table below, determine P(X = 1, Y = 7). 3 | 5 7 0.15 0.050 0.3 0.15 0.05 0.15 0.05 0.1 a) 0.1 b) 0.3 c) 0.45 d) 0.15 e) 0.35 f) None of the above.
Please find and classify all the critical points for Q19 and Q20 5-20 Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function 5. f(x, y) xy y + y 6. f(x, y)-xy 2x 2y x-y 7. f(x, y) x-y)1 - xy) 8. f(x, y)y(e- ) 9. f(x, y)-x y* + 2xy 10. f(x,...
Let X and Y have the following joint distribution: X/Y -1 1 0 0.2 0.15 2 0.1 0.2 4 0.25 0.1 a) Find the probability distributions for X and Y b) Find E[X] and E[Y] c) Find the probability that X is larger than 1 d) Find E[XY]