Suppose that x and y are independent random variables having...

Suppose that X and Y are independent random variables having the joint probability distribution x f(x, y) 2 4 1 0.10 0.15 y 3 0.20 0.30 5 0.10 0.15 Find (a) E(2X − 3Y ); (b) E(XY ).

Transcript

00:01 Hello, schwentz.

00:02 We are going to write here, suppose that x and y are independent random variables having the joint probability distribution.

00:08 This is our table.

00:09 We are going to find expectation in both the cases, expectation of 2x minus 3y, an expectation of x, so basically we are going to write here for this.

00:18 In the very first case, what would be our expectation of this must be erased? what would be our expectation of 2x minus 3y? so this value must be written as sigma.

00:32 Sigma of if i write here for this this must be sigma of sigma of sigma of so x and y so if i write here for this g of x y g of x y and f of xy so if i write here for this this must be written as here this must be written as g of xy that must be equivalent to 2x minus 3y so basically if i write here for this expectation of 2x minus 3y, 2x minus 3y, if i write here for this.

01:09 So if i write here 3y, that is equivalent to, that must be equivalent to, we are writing here sigma of sigma of x and y, 2x minus 3y.

01:27 So let's erase this to make it more clear, 2x minus 3y.

01:32 So let's erase this to make it more clear.

01:32 We are going to write here f of x y this must be f of x y so this is 2 multiplied by 2 minus 3 multiplied by 1 3 multiplied by 1 so this must be 0 .1 0 plus 2 so this must be erased here 2 multiplied by 4 minus 3 multiplied by 4 minus 3 multiplied by 1 and this must be multiplied by 0 .15 and this is 2 multiplied by 2 minus 3 multiplied by we are going to write here 3 multiplied by 3 and this must be multiplied by this must be multiplied by 0 .20 and if i write here this must be again 2 multiplied by 4 minus 3 multiplied by 3 and this must be multiplied by 0 .30.

02:36 So if i write here, this must be 2 multiplied by 2 multiplied by 2 minus 3 multiplied by 5.

02:46 So if i write here for this, this must be multiplied by 0 .10.

02:51 So basically if i write here for this 2 multiplied by 4, 2 multiplied by 4 minus 3.

02:58 Multiplied by 2 and this must be multiplied by this must be multiplied by 0 .15 so this total value must be calculated as 0 .10 plus 0 .10 plus 5 multiplied by 0 .5 plus minus 5 multiplied by 0 .20 multiplied by 0 .20 plus 5 multiplied by 0 .20 and this is minus 1 multiplied by 0 .30.

03:33 So if i write here, this is minus 11 multiplied by 0 .10.

03:38 So let's erase this to make it more clear, minus 11 multiplied by 0 .10 plus minus 7 multiplied by 0 .15...

Question

Suppose that X and Y are independent random variables having the joint probability distribution x f(x, y) 2 4 1 0.10 0.15 y 3 0.20 0.30 5 0.10 0.15 Find (a) E(2X − 3Y ); (b) E(XY ).

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