Easiest way:
Look at A and C. To get from A to C you need 6 steps to the right and 2 steps upwards.
Slope means (in layman's terms) that how many steps you take upwards when you take 1 step to the right.
In your case you take 2/6 steps, because it would take you 6 steps to the right to go 2 steps upwards.
A slope of 4 would mean that 1 step to the right is followed by 4 steps upwards. A slope of -5 means 1 step to the right, 5 steps downwards.
To get from A to E you need 9 steps to the right and 3 steps upwards. This means a 3/9 slope. The simplest form of it is 1/3.
1/3 slope means that for every 3 steps to the right you take 1 step upwards.
I hope this was understandable, this is how they taught me this in 5th grade more than a decade ago.
(y=mx+b) Where m is slope and b is y-int.
y=-5/6x-1
The line of reflection is at 5 on the x-axis. C is at the point,(6,2)
The first one. The second looks like (p-6)+2. The third looks like (2-p)6. And the fourth looks like 6+ (2+p)
<em>Y</em>₁ and <em>Y</em>₂ are independent, so their joint density is
By definition of conditional probability,
P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = P((<em>Y</em>₁ > <em>Y</em>₂) and (<em>Y</em>₁ < 2 <em>Y</em>₂)) / P(<em>Y</em>₁ < 2 <em>Y</em>₂)
Use the joint density to compute the component probabilities:
• numerator:
• denominator:
(I leave the details of the second integral to you)
Then you should end up with
P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = (1/6) / (2/3) = 1/4
