Exercise 10.3. Toss a coin three times. Let X{0,1,2} be the number of Heads in the first two
tosses. Let Y{0,1,2} be the number of Heads in the last two tosses. Find the joint probability
function of X and Y (compare the table in Section 10.4 of the Lecture Notes). Are X and Y
independent? Exercise 10.4. Let X and Y have joint density f(x,y)=1/4 for 11) Exercise 10.5. Let
X and Y have joint density function c(2x+y2) on R={(x,y)021X). Exercise 10.6. For X and Y as
in the previous exercise, find P(X<1) and P(Y<21/X<1) Exercise 10.7. Let X1,X2,X3 and X4 be
independent exponential random variables, each with parameter and let V=max{X1,X2,X3,X4}
and W=min{X1,X2,X3,X4}. Find P(V>2/) and P(W>2/). Exercise 10.8. (Bonus) Suppose X and
Y have joint density f(x,y)=2 for 0.
Exercise 10.3. Toss a coin three times. Let X{0,1,2} be the number of.pdf
1. Exercise 10.3. Toss a coin three times. Let X{0,1,2} be the number of Heads in the first two
tosses. Let Y{0,1,2} be the number of Heads in the last two tosses. Find the joint probability
function of X and Y (compare the table in Section 10.4 of the Lecture Notes). Are X and Y
independent? Exercise 10.4. Let X and Y have joint density f(x,y)=1/4 for 11) Exercise 10.5. Let
X and Y have joint density function c(2x+y2) on R={(x,y)021X). Exercise 10.6. For X and Y as
in the previous exercise, find P(X<1) and P(Y<21/X<1) Exercise 10.7. Let X1,X2,X3 and X4 be
independent exponential random variables, each with parameter and let V=max{X1,X2,X3,X4}
and W=min{X1,X2,X3,X4}. Find P(V>2/) and P(W>2/). Exercise 10.8. (Bonus) Suppose X and
Y have joint density f(x,y)=2 for 0
