2

# Question 1 (10 marks)Let the two random variables X and Y have the following joint probability density function (pdf)k + y; if 0 < I < 2,2 < y < 1 fx(â...

## Question

###### Question 1 (10 marks)Let the two random variables X and Y have the following joint probability density function (pdf)k + y; if 0 < I < 2,2 < y < 1 fx(â‚¬,y) = 0; otherwiseDraw diagram of the joint sample space of X and Y.markb) Show that k2marks)Find the marginal probability density functions fx (1) and fy (y).2 marks)Calculate E(X) and E(Y):2 marks)Find the conditional density function fxi(cly). If applicable; state the interval(s for which your function applies; and the value of fx

Question 1 (10 marks) Let the two random variables X and Y have the following joint probability density function (pdf) k + y; if 0 < I < 2,2 < y < 1 fx(â‚¬,y) = 0; otherwise Draw diagram of the joint sample space of X and Y. mark b) Show that k 2 marks) Find the marginal probability density functions fx (1) and fy (y). 2 marks) Calculate E(X) and E(Y): 2 marks) Find the conditional density function fxi(cly). If applicable; state the interval(s for which your function applies; and the value of fxjy (xly) outside the interval(s) You do not need to calculate fyix(ylx). mark) Find the conditional expectation E(XIY ) mark Are X and Y independent? Justify your answer mark)  #### Similar Solved Questions

##### Brz2)2 equiv. NaNHzexcess NaNHzCH;BrHAO. HzSO4, HgSOaNaBHaLI; NHa () HOz NaOH; HzoCHCH_BrHBrHz Lindlar cetalyst BHJTHFPBrJ
Brz 2) 2 equiv. NaNHz excess NaNHz CH;Br HAO. HzSO4, HgSOa NaBHa LI; NHa () HOz NaOH; Hzo CHCH_Br HBr Hz Lindlar cetalyst BHJTHF PBrJ...
##### Question 32.5 ptsConsider a differential equation y =2 y + 1. What is the equation of the tangent Iine to the solution curve at (1,2)?y = â‚¬ + 1y =-c +3y = 2xy = 2
Question 3 2.5 pts Consider a differential equation y =2 y + 1. What is the equation of the tangent Iine to the solution curve at (1,2)? y = â‚¬ + 1 y =-c +3 y = 2x y = 2...
##### Finp 2 LI Soc X'=AxA: (2 4) 70 2 L-I_ ELn_ " 7A7A= ( ;) Ft-D 2 ReA=(41) â‚¬= Civer Sol: X'=At AzC &(51 7 2 %t FIND Palnculp? co1 Xp F2 Tte 4DC {At-t
Finp 2 LI Soc X'=Ax A: (2 4) 70 2 L-I_ ELn_ " 7A7 A= ( ;) Ft-D 2 Re A=(41) â‚¬= Civer Sol: X'=At AzC &(51 7 2 %t FIND Palnculp? co1 Xp F2 Tte 4DC {At-t...
##### (Lectute Exam ApII 0321202Item 34 eppropr
(Lectute Exam ApII 0321202 Item 34 eppropr...
##### A sln contains 7.88g of carbonic acid.How many equivalentsare in the sln?
a sln contains 7.88g of carbonic acid.How many equivalents are in the sln?...