00:01
Hello students, to prove the properties, we will use the properties of expected value i .e.
00:05
Mean and the variance to exploit the fact that x and y are independent random variables.
00:10
Let's start from the first bit i .e.
00:12
E of xy is equal to e of x into e of y.
00:19
By definition, the expected value of a random variable x is given by e of x is equal to summation x, x into p, x equal to x.
00:30
For the product of x and y, we have e of xy equal to summation x, summation y, x into y into p, where x equal to x and into p, where y equal to y.
00:46
Let's interchange the summation order.
00:50
So, we have e of xy equal to summation x, x into p, x equal to x into summation y, y into p into y equal to y.
01:04
So, this is equal to e of x into e of y.
01:07
So, we can write this is prove that e of xy equal to e of x into e of y...