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Question 2 2.1 Solve the below problem (show all calculations). Let Y, and Y, be random variables with joint density function 2, 0 s y, s 1, 0 syz s 1, 0

Question 2 2.1 Solve the below problem (show all calculations). Let Y, and Y, be random variables with joint density function 2, 0 s y, s 1, 0 syz s 1, 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Question 2 2.1 Solve the below problem (show all calculations). Let Y, and Y, be random variables with joint density function 0 < y, < 1, 0, 0 s y2 S 1, 0<Y2 + y1 < 1 2, elsewhere. The marginal density function of f(y1) = 2(1 – y,), 0 <y, < 1 Identify the distribution of the marginal density function f (y1) and use it to find the E(Y,) and V (Y,). 2.2 Solve the below problem. Table 1 contains the probabilities associated with each possible pair of values for Y, and Y2 and is known as the joint probability function for Y,and Y2 Table: Probability function for Y, and Y2 | Y2 | 0 |1 2 1/9 2/9 1/9 1 2/9 2/9 0 1/9 0 Find F (1, –2) and F(3,3). 2.3 BP petrol is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Consider the joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week and Y2, the proportion of the capacity sold during the week, given by f(Y1, 92) = {0 3y1, 10, 0 < y2 < Y1 S 1, elsewhere.
Transcribed Image Text:Question 2 2.1 Solve the below problem (show all calculations). Let Y, and Y, be random variables with joint density function 0 < y, < 1, 0, 0 s y2 S 1, 0<Y2 + y1 < 1 2, elsewhere. The marginal density function of f(y1) = 2(1 – y,), 0 <y, < 1 Identify the distribution of the marginal density function f (y1) and use it to find the E(Y,) and V (Y,). 2.2 Solve the below problem. Table 1 contains the probabilities associated with each possible pair of values for Y, and Y2 and is known as the joint probability function for Y,and Y2 Table: Probability function for Y, and Y2 | Y2 | 0 |1 2 1/9 2/9 1/9 1 2/9 2/9 0 1/9 0 Find F (1, –2) and F(3,3). 2.3 BP petrol is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Consider the joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week and Y2, the proportion of the capacity sold during the week, given by f(Y1, 92) = {0 3y1, 10, 0 < y2 < Y1 S 1, elsewhere.
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