00:01
So for the part a, you've been given xi is uniformly distributed on the range of negative 1 and 3.
00:10
So we get f of xi to be 1 over v minus a, which is 1 over 3 minus minus 1.
00:19
So you have 1 over 4.
00:21
So the pdf of a uniform distribution we know to be this on the range of a or x line between x.
00:30
X like between a and b inclusive so now we have y i to be negative 2 log x i plus 1 over 4 for i from 1 2 to 8 so this implies getting y 1 to be minus 2 log x i x1 plus 1 over 4 so now you have to find the distribution of of y 1 so we get minus y 1 over 2 is equal to the log of x1 plus 1 over 4 so we get e to the power minus y and y 1 and 2 is equal to e to the power the log of x1 plus 1 on 4 so we are going to get 4 e to the power minus y1 on 2 minus 1 is equal to x1 so we get the the x1 over the y 1 to be equal to 2 let me write 4 e to the ball minus y 1 on 2 then you have x minus times x you have minus 1 on 2 so we get minus 2 e to the bar minus minus this is times minus minus to e to the power minus y one on two so the pdf of y1 will be jing of y to be called f of x you know it's the absolute or the d x over d y 1 so we get j of y to be equal to f of x the absolute of negative 2, e to the bar minus y1 and 2, which is equal to 1 over.
03:36
You have 1 over 4 times 2 x, e to the bar minus y1 and 2.
03:50
So we get 1 on 2, e to the power minus y1 on 2.
03:58
So this is the pdf of all.
04:02
Hence, we can see that this follows an exponential distribution with mean of 2.
04:10
So for the part b, exponential distribution has an additive property.
04:17
So here we have y1, y2 are exponential...