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NIELIT STA 2021

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Let X be uniform random variable on [0,4] and Y be uniform random variable on [0,1]. If X and Y are independent, then P(max [X,Y] > 3) is equal to: 

 

  1. 1 / 4
  2. 1 / 2
  3. 1 / 8 
  4. 1

1 Answer

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Firstly, as the range in an interval is provided, it mean s it's a continuous random variable..
(Consider them like intervals... 4 in X and 1 in Y)...

Now, we kniw that in Y there's no possible outcome to be greater than 3..

So, P(max(x,y)>3) =(1 - P(x<=3) * P(y<=3)) = 1 - (3/4) * 1 = 1/4... 

Also can be calculated as...
P(max(x,y)>3) = P(x>3) * P(y<=x | x>3) = 1/4 * 1 = 1/4..

So, Option A = 1/4 is correct

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