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!