joint probability question

[gk]

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[knowpraveen]

Are you talking about the 3rd question in the image? This could solved graphically. Plot a graph of X+Y=1 since we are given the density function.

It's obviously a uniform distribution function, the area of the region under consideration is 1/2, therefore the density turns out to be 1/(1/2) =2 for x>0, y>0 and X+Y<1. I hope, the question stands clear now. So, for P(X<2Y) Draw another line X-2Y=0 which is a positively sloped line passing through the origin meeting the X+Y=1 line at (2/3,1/3). Integration (1-x-x/2) from 0 to 2/3 which yields 1/3. Hence the probability of the case in question is 1/3/(1/2) = 2/3

Correct me if I'm wrong.

[varnika1880]

Can u plz provide a link or name of the concept u used coz this seems relatively easier way of calculating such prob questions ..thnx

[knowpraveen]

This stems from the definition of uniform distributions. Just like we use the image of a straight line to picture a monovariate distribution, for a bivariate distribution it's really going to save our time if we use the co-ordinate axes.

See if this helps.

http://www.math.illinois.edu/~ajh/370/problemsets/problemset4.pdf

And, the solutions - http://www.math.illinois.edu/~ajh/370/problemsets/problemset4s.pdf

[varnika1880]

Yes it is ..but m really stuck at  bivariate  distribution questions .(confused with the concept )...similar ques was there in mock 1 of  dse super 20

[knowpraveen]

Do the given actuarial workouts. You'll be able to figure it out. God speed. They have provided detailed solutions to each and every question.

[gk]

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