Points
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1. ln a certain study, families consisting of exactly 5 members are considered. Suppose it is known
that exactly two people in each family are employed. Two members of each family are randomly
called, and asked whether they are em
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m Cw [m]: Cw[é-2+M,?] = saVIz,z)+c.w1u,a}:,/§=g
q- 61 W ?
2 O
/\(=E\r[(]=EY[%?tU3=%_EY[?3+EF[LAJ :ME
A O
d=%/A_}q/Az =7 929 = E Yf? :iz
01$: CWHK): Cw[x, ghoc] : ._§,.r awful + CWNM]
o = Cw[vw)+ emu] thul
W M
D
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'. OZY=é CSVDCL'Z') : .3: C641 [2*4 '
x = y = as.vector( c(1:4)
one = rep(1,4)
fxy = matrix(c(1,1,1,1, 1,0,0,0, 1,0,0,0, 1,1,1,1), nrow=4, ncol=4, byrow=T)
fxy = fxy/sum(fxy)
fx = fxy %*% one
# one marginal
fy = t(one) %*% fxy
# the other marginal
fx = as.vector(fx)
# R thinks fx is matrix. F
Stat 509/Econ 580: Econometrics 1
Midterm Practice Problems and Solutions
Solution:
To get a pattern of hhh, all that matters is the outcome of the last couple of tosses. For example, getting
a sequence of ththtthh is no dierent than a sequence of hhthh a
jpeg("exp.jpg")
dat = rexp(1000,2)
hist(dat, freq=F)
x = seq(0,4,.01)
f = dexp(x,2)
lines(x,f, col=2)
dev.off()
Consider a population consisting of n objects. If we take a sample of size m
from this population (without replacement), then there are nCm (re