00:01
Students, let me explain to the question.
00:04
So here, if we draw two random numbers x and y, so here two random numbers x and y, they are each distributed uniform.
00:15
So these two numbers, they are distributed uniform on the interval of uniform, that is 0 .1.
00:28
So if these two variables that is these two random numbers they are independent these two random numbers they are independent what is the probability that they product x into y so probability of product x into y it is greater than one divided by two so this this question they have was to have to find out the probability that the product of random numbers that is x into y it is greater than 1 by 2.
01:08
So coming to the solution here, here we can at least work out the distribution of two uniform variables, that is 0 comma 1 variables, x1 and x2, x1 and x2.
01:28
So let here, z is equal to x1 into x1.
01:34
So now the density of z density of z is equal to fz into z that is equal to minus log z here it is more than 0 and it is less than plus 1 that is 1 now if it is the case then p z it is more than 1 that is more than 1 by 2.
02:12
So that is equal to 1 minus p into z it is less than or equal to 1 by 2.
02:20
That is equal to 1 minus f 1 by 2.
02:24
That is equal to 1 minus integral 0 to 1 by 2 minus 1 by 2 minus log z into d z.
02:35
So now we know the integration...