2. Show the marginal pdf of X and Y. 3. Find P(X > 1/2, Y < 1).

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...
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#2 and #3 of Example 2.6
Example 2.6. Let X and Y be jointly continuous random variables with joint PDF is given by:
fx,Y (r, y) = k(1 +x²y)I0,1)(x)I(0,2)(y)
1. Solve for k to make it a valid pdf.
1 =
1 =
k(1+ x?y)dxdy
1
1 =k
x +
dy
3
1 =k
+ 의 dy
1 =k
1 =k |2+
1 =
3
k =
8
2. Show the marginal pdf of X and Y.
3. Find P(X > 1/2, Y < 1).
Transcribed Image Text:Example 2.6. Let X and Y be jointly continuous random variables with joint PDF is given by: fx,Y (r, y) = k(1 +x²y)I0,1)(x)I(0,2)(y) 1. Solve for k to make it a valid pdf. 1 = 1 = k(1+ x?y)dxdy 1 1 =k x + dy 3 1 =k + 의 dy 1 =k 1 =k |2+ 1 = 3 k = 8 2. Show the marginal pdf of X and Y. 3. Find P(X > 1/2, Y < 1).
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