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Question 1

R1 ~ N(6,196)
R2 ~ N(15,1024)
rho = .7


q1:
mean of R1 is 6

q2:
sd of R1 is 
> sqrt(196)
[1] 14

q3:
s1 = 14
s2 = 32
cov = .7*s1*s2
cov
313.6

q4:

> 1 - pnorm(0,6,14)
[1] 0.6658824

q5:
pnorm(10,15,32) - pnorm(0,15,32)
> pnorm(10,15,32) - pnorm(0,15,32)
[1] 0.1182938

q6:
P = .2 * R1 + .8 * R2

mean of P:
.2*6 + .8*15

> .2*6 + .8*15
[1] 13.2

q7:
sd of P:

sqrt(.2^2 * 196 + .8^2 * 1024 + 2*.2*.8*313.6)
> sqrt(.2^2 * 196 + .8^2 * 1024 + 2*.2*.8*313.6)
[1] 27.63244

q8:
mp = 13.2
sdp = 27.63244

P(P>0)
1-pnorm(0,mp,sdp)
> 1-pnorm(0,mp,sdp)
[1] 0.6835679

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Question 2


q9:
34/sqrt(35)

> 34/sqrt(35)
[1] 5.747049

q10: 
se = 5.57
18+2* se

> 18+2* se
[1] 29.14

q11:

phat = .77
sephat = sqrt(phat*(1-phat)/35)
sephat
> sephat
[1] 0.07113368