Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a big law firm: An Ben and Cameron (abbreviated to A,B and C). Let X₁ denote the number of contracts assigned to Anna a X₂ denote the number of contracts assigned to Ben. For some reason, completely beyond my control, we a not interested in Cameron's escapades. 1. Find the joint probability function of X₁ and X₂. 2. Find the marginal distribution fx₁ (1₁) of X₁ and the marginal distribution fx,₂ (1₂) of X₂. 3. Are X and Y independent? Give reasons.
Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a big law firm: An Ben and Cameron (abbreviated to A,B and C). Let X₁ denote the number of contracts assigned to Anna a X₂ denote the number of contracts assigned to Ben. For some reason, completely beyond my control, we a not interested in Cameron's escapades. 1. Find the joint probability function of X₁ and X₂. 2. Find the marginal distribution fx₁ (1₁) of X₁ and the marginal distribution fx,₂ (1₂) of X₂. 3. Are X and Y independent? Give reasons.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Question
sub questions 1, 2 and 3 please
![Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a big law firm: Anna,
Ben and Cameron (abbreviated to A,B and C). Let X₁ denote the number of contracts assigned to Anna and
X₂ denote the number of contracts assigned to Ben. For some reason, completely beyond my control, we are
not interested in Cameron's escapades.
1. Find the joint probability function of X₁ and X₂.
2. Find the marginal distribution ƒx₁ (7₁) of X₁ and the marginal distribution fx₂ (₂) of X₂.
3. Are X and Y independent? Give reasons.
4. Calculate the expected values E(X), E(Y) and the variances V ar(X), Var(Y).
5. Calculate the covariance Cov(X₁, X2) of X₁ and X₂ . Hint: Use definition
-
Cov(X,Y) = E[(X – E(X))(Y – E(Y))]ΣΣ(x − E(X))(y − E(y) * f (x, y))
х у](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2Fee7c6022-57cb-49dd-adf6-9dc90dff786a%2Fa6zyegl_processed.png&w=3840&q=75)
Transcribed Image Text:Two criminal cases/law suits are randomly assigned to one or more of three lawyers in a big law firm: Anna,
Ben and Cameron (abbreviated to A,B and C). Let X₁ denote the number of contracts assigned to Anna and
X₂ denote the number of contracts assigned to Ben. For some reason, completely beyond my control, we are
not interested in Cameron's escapades.
1. Find the joint probability function of X₁ and X₂.
2. Find the marginal distribution ƒx₁ (7₁) of X₁ and the marginal distribution fx₂ (₂) of X₂.
3. Are X and Y independent? Give reasons.
4. Calculate the expected values E(X), E(Y) and the variances V ar(X), Var(Y).
5. Calculate the covariance Cov(X₁, X2) of X₁ and X₂ . Hint: Use definition
-
Cov(X,Y) = E[(X – E(X))(Y – E(Y))]ΣΣ(x − E(X))(y − E(y) * f (x, y))
х у
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