Quiz 2 Solutions, XP Stats 2015
Question 1
1.1
.21
1.2
.27+.49
[1] 0.76
1.3
.49/(.21+.49)
[1] 0.7
1.4
No, P(Y=1) is not the same as P(Y=1|X=1).
1.5
Yes because it is 0 or 1.
1.6
P(X=1) =
.21+.49
[1] 0.7
so E(X)=p=.7
1.7
P(Y=1) = .76.
P(X=1) = .7.
Intuitively, closer p is to .5, the bigger
the variance so Var(X) is bigger.
or.
> .7*.3
[1] 0.21
> .76*.24
[1] 0.1824
Question 2
2.1
.5
2.2
.68
2.3
(1-.68)/2
[1] 0.16
2.4
.025
2.5
.5
2.6
.68
2.7
.16 if you used $X$ and 1 if you used Z.
2.8
.025 if you used $X$ and 0 if you used Z.
Note that 2.1-2.4 and 2.5-2.8 have the same answers because,
in a sense, they are the same questions!