DSE 2011

[s]

8.suppose the estimated regression eqaution is lny=1.2+0.5x .which is a good interpretation of estimated relationship between x and y:

a.a unit change in x associated with a 50% change in y
b. unit change in x associated with a 0.5% change in y
c. a 1% change in x associated with a 50 unit chng in y
d. a 1 % chng in x associated with a 0.5 unit chng in y



also:

if a man has 3 children and its known atleast one of them is a boy,then what is the probability that he has 2 boys 1 girl: ans is 1/3

but if we consider sample space to have 8 elements keeping in mind the order the children are born then shouldnt answer be 3/7?

[s]

if someone knows how to go about these please respond

[rahul]

for the first one 1% change in x will lead to 50% increase in y
Just diff w.r.t. to x
for second one sample space{(3b,0g),(2b,1g),(1b,2g),(0,3g)}
so ans is 1/3

[s]

@ rahul thanks ..

yeah if we take sample space to be {bbb,bgg,bbg,ggg} then answer is 1/3 but if u look at DSE 2009 problem 18 Part II : youve been told that a family has 2 children and one of them is a daughter,then probability the other is a daughter too? ans is 1/3 because we take sample space { bb,bg,gb,gg} ..so y shudnt we take the 8 element sample space here?..i mean i find it a bit contradictory

[rahul]

the difference between two sample space may be
1st one is sample space of no. of boys and girls
and 2nd one is sample space of boys & girls.
not sure bcoz I also get confuse between these two.

[Amit Goyal]

Given the problem, Answer is 3/7.

[s]

thank u so much sir!!