ISI 2009

[Ram]

1. Two persons, A and B, make an appointment to meet at the train station
between 4 P.M. and 5 P.M.. They agree that each is to wait not more than 15
minutes for the other. Assuming that each is independently equally likely to
arrive at any point during the hour, find the probability that they meet.
A. 15/16
B. 7/16
C. 5/24
D. 22/175


3. A box contains 100 balls. Some of them are white and the remaining are
red. Let X and Y denote the number of white and red balls respectively. The
correlation between X and Y is
A 0.
B 1.
C −1.
D some real number between −1/2 and 1/2

[neha]

question 3:
here x + y =100 , so the number of white balls and the number of red balls have a perfect negative correlation, hence the answer should be -1.

[Ram]

Hi Neha, tell me how do you know that it is perfectly negative correlation???

[neha]

so for example if u draw a scatter diagram,, and all the points lie on the same line,, we say that the variables are perfectly related, as in case as x increases , y decreases, there will be negative correlation and perfect as has already been said,, so -1.  

[Ram]

Thank you :)

[seema]

Let X - no. of min past 4pm A arrives
Y - no. of min past 4pm B arrives
a = 240  b= 360
f(X)=1/60   f(Y)=1/60
f(X,Y)= 1/f(X).f(Y)= 1/3600


Req prob= P(X+15>Y) or P(Y+15>X)  = 2 P(X+15>Y)
            = 1- 2 P(X+15<Y)

P(X+15<Y) = integrate f(X,Y), X tending from 0 to (Y-15) & Y tending from 15 to 60.
               = 9/32

hence, Req prob = 1-2(9/32) = 7/16.