Suppose f(x,y)=(1/8)(6-x-y) for 0<x<2 and 2<y<4.
If all else is the same, then why can’t x be defined on the
range [0,3]?
Find p(0.5 < X < 1, 2 < Y < 3)
Find fX(x) and fY(y)
Are X and Y independent? Why or why not?
Find p(0.5 < X < 1) and p(2 < Y < 3)
Find p(Y<3|X=1)
Find p(Y<3|0.5<X<1)
4.
a. Suppose Z~Normal(0,1). Find P(1<Z<2). (3pts)
b. Suppose X~Normal(-2,1). Find P(X>0 or X<-3). (3pts)
c. Suppose X~Normal(2,4). The middle 88% of the X values are
between what two values? (3pts)
x
y
fxy(x,y)
-1
-2
1/8
-0.5
-1
1/4
0.5
1
1/2
1
2
1/8
Show that the function above satisfies the probabilities of a
joint probability mass function.
Find E(X), E(Y), V(X), V(Y)
Find marginal probability distribution of X
Find the covariance and correlation.
4. The joint density function of (X, Y ) is
f(x,y)=2(x+y), 0≤y≤x≤1
. Find the correlation coefficient ρX,Y
.
5. The height of female students in KU follows a normal
distribution with mean 165.3 cm and s.d. 7.3cm. The height of male
students in KU follows a normal distribution with mean 175.2 cm and
s.d. 9.2cm. What is the probability that a random female student is
taller than a male student in KU?