00:01
Hi, i'm david and i'm here and i'm here here i'm here here given the john density function on the x and y equal to the sum constant c times in the x plus y where we have the x equal to 1 and 2 and y equal to the zone 1 so let me try to draw the table on the probability for the x and y and here we have this one will be in the x and has a volume of the 1 and 2 this will be the y has a value under zone 1 and here we will have the first one under zero zero if we apply this one into the function and then we get equal to the 1 and 0 and then we get equal to the 1c this only have the 2c this only have the 2c this only have the 3c and we require then the total sum that it must equal to the 1 therefore if we add them up we have 1c plus 2c plus 2c plus 2c plus 3 and must exactly equal to 1 and from here we get equal to the 5 plus 3 could be the ac equal to 1 therefore the c must equal to 1 out of 8 and equal to 0 1 25 and that will be the answer for the first one we have found the c there and when we get the c we can put it back to again the probability here so this one will be equal to the 1 will be the 0 1 25 times 2 will equal to the 0 bond.
01:46
So i will have here 0 .125 times 2 equal to the 0 .25.
01:56
This is an answer 025 and then we will have equal to the 0 .375.
02:07
And that will be the summary of the probability.
02:10
Now from here we can find the density of the x.
02:15
So x can take the volume of 1 and 2 this will be the probability of x so it will end up on the row there so it will try to add them up which we get this one will equal to the 0 .375 and the next one we have us when the 0 .25 equal to the 0 .6 25 similarly 1 to 5 for the y.
02:44
Y will have the value of the zone 1 and probability in the y.
02:51
They will add them up on the column.
02:56
And then we get this one will be the 0 .375.
03:00
Sorry, this one will be 0 .1 25 plus 0 .25 will equal to 0375.
03:12
And this one will equal to the 0 .625.
03:15
And that we have to be able to find the answer for the question a.
03:20
125 e of the x.
03:22
So if the x we will multiply them like a pair and then we add them up.
03:26
Then we have the 0 .375 times 1 plus 2 times 0 .625 and then we get equal to plus 2 times 0 .625 equal to the 1 .625 and for the e of the y, a variant of the x, that equal to here, let me think the calculator and compute this one and for the variance it will equal to the first value will be x equal to the 1 we minus the mean squared up times in the cost of probability it will be 0 .3 plus the next volume will be the 2 minus the mean square times under 0 .6 .25...