A group of 9 friends includes 4 Americans, 2 Canadians, and 3 Italians. Three friends are...

A group of 9 friends includes 4 Americans, 2 Canadians, and 3 Italians. Three friends are to be selected at random for a trip. Let X denote the number of Americans and Y be the number of Canadians selected at random among the three friends selected for a trip.

1) Find the joint probability density function of the random variables X and Y and the marginal density functions.

2) Find Cov(2X-1, -Y+1).

Expert Solution

orchestra answered 2 years ago

a = [4, −9, 4] b = [7, 2, 3] c = [5, −8, 9] d...

a = [4, −9, 4] b = [7, 2, 3] c = [5, −8, 9] d = [1, −3, 2] e = [6, −2, −5, 9] f = [4, −3, 7, 5] g = [1, 3, −1, 5] h = [7, −5, 5] i = [5, 13, −7, 11] Express the hyperplane implicitly or explicitly given the following a) a and h b) f and i c) e, f, and g d) The hyperplane containing b, c and d can...

(10 pts) For the following data: Group 1 Group 2 3 5 2 9 1 8...

(10 pts) For the following data: Group 1 Group 2 3 5 2 9 1 8 8 12 4 9 Calculate the following: SS1 SS2 SSD SD Sx1-x2

[ 1 -1 3 -3 5 2 ] A=[ 1 -1 4 -1 9 -4 ]...

[ 1 -1 3 -3 5 2 ] A=[ 1 -1 4 -1 9 -4 ] [ -1 1 -3 3 -4 8 ] [7] b=[5] [4] use the row reduction algorithm to solve the following Describe the solution set of Ax=b in parametric vector form describe the solution set of Ax=0 as Span[ V1,V2,....,Vp]

4. [22 pts] For the function ?(?) = 2?5 − 9?4 + 12?3 − 12?2 +...

4. [22 pts] For the function ?(?) = 2?5 − 9?4 + 12?3 − 12?2 + 10? − 3 answer the following: a. [2 pts] Determine whether the function represents a polynomial. Justify your answer. b. [4 pts] Determine whether the function satisfies the Intermediate Value Theorem on the interval [0, 5]. Justify your answer. c. [2 pts] Determine the number (quantity) of complex zeros that the function has, provided the each zero is counted by its multiplicity. d. [4...

2. A group of 24 physical doctors from three countries consists of 7 Americans, 8 British...

2. A group of 24 physical doctors from three countries consists of 7 Americans, 8 British and 9 Chinese. They (wearing masks) are seated at random around a (large enough) table to discuss the means of treatment of COVID-19 patients. Compute the following probabilities: (a) that all the Americans sit together; (b) that all the Americans and the British sit together; (c) that all the Americans, all the British and all the Chinese sit together. (d) Randomly choose 6 doctors...

How to make TABLE OF DIHEDRAL GROUP 10? group theory D10: e,a,a^2,a^3,a^4,b,ba,ba^2,ba^3,,ba^4

Matrix A2= [1 2 3; 4 5 6; 7 8 9; 3 2 4; 6 5...

Matrix A2= [1 2 3; 4 5 6; 7 8 9; 3 2 4; 6 5 4; 9 8 7] Note: TA2 is defined to be a linear transformation that maps any vector x to A2* x. That is TA2 = A2*x. Also the range of the Linear transformation represented by A2 is the same as the column space of A2. l) Find a basis for the null(TA2). m) Find nullity of A2, TA2 and A2tA2. n) Find rank(A2), rank(A2t),...

Student Gender Hours online/week Friends 1 Female 9 100 2 Female 5 60 3 Female 2...

Student Gender Hours online/week Friends 1 Female 9 100 2 Female 5 60 3 Female 2 50 4 female 12 110 5 male 4 50 6 female 2 80 7 male 10 450 8 female 7 90 9 female 2 30 10 female 4 150 11 female 12 380 12 male 7 120 13 female 6 80 14 male 3 200 15 male 8 430 16 female 7 170 17 male 4 90 18 female 6 240 19 female 4...

An urn contains 4 red, 5 blue, 2 yellow, and 9 green balls. A group of...

An urn contains 4 red, 5 blue, 2 yellow, and 9 green balls. A group of 5 balls is selected at random without replacement. What is the probability that the sample contains: a. atleast one of each color? b. at most 3 green balls?

x 2 8 5 9 4 3 9 6 7 8 y 3 6 5 7...

x 2 8 5 9 4 3 9 6 7 8 y 3 6 5 7 9 7 4 6 9 9 -5.48x + 0.17 5.48x + 0.17 -0.17x + 5.48 0.17x + 5.48

Question