If X is the proportion of persons who like pudding n’ souse, Y
is the proportion of persons who like
mauby, and the joint probability density of X and Y is given
by:
f (x) =
Find the probabilities that:
(i) no more than 30% like pudding n’ souse. [8 marks]
(ii) at least 50% like mauby given that 20% like pudding n’
souse.
Homework Answers
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If X is the proportion of persons who like pudding n’ souse, Y
is the proportion...
The probability density function of X is given by 0 elsewhere Find the probability density function...
The probability density function of X is given by
0 elsewhere
Find the probability density function of Y = X3
f(r)-(62(1-x)for0 < x < 1
2nd pic is answer. show the work plz 13 Let X and Y have the joint...
2nd pic is answer.
show the work plz
13 Let X and Y have the joint probability density function ,흄.ru2 for 0 < x < y. < 2 f(x,y) = elsewhere What is the joint density function of U it is nonzero? 3X-2Y and V-X + 2Y where 687 Probability and Mathematical Statistics 32768 13° g(u,t) = 0 otherwise.
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
4. Let X and Y have joint density function le-x 0 < y < x <...
4. Let X and Y have joint density function le-x 0 < y < x < 0 Jxy(x, y) = lo elsewhere Another random variable of interest is U=X–Y. Find the probability density function for U.
) Let X, Y be two random variables with the following properties. Y had density function...
) Let X, Y be two random variables with the following
properties. Y had
density function fY (y) = 3y
2
for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given
Y = y, X
had conditional density function fX|Y (x | y) = 2x
y
2 for 0 < x < y and zero elsewhere.
(a) Find the joint density function fX,Y . Be precise about where
the values (x, y) are non-zero....
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
If X and Y have a joint density given by f(x, y)- 2, for 0 <...
If X and Y have a joint density given by f(x, y)- 2, for 0 < y < x < 1 0, elsewhere (a) If V - -InX, what is the density of V? (b) If V -InX and W X + Y, what is the joint density of V and W? Sketch the region for which the joint density is nonzero
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2)...
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
5. If two random variables X and Y have the joint density k(52+2y2) for 0<<2 0...
5. If two random variables X and Y have the joint density k(52+2y2) for 0<<2 0 <y< 1 f(r, y) elsewhere (a) Find k (b) Find P(0<x< 1, 0<Y<0.5) (c) Find marginal density fi(a) and f2(y) (d) Are X and Y independent? (e) Find E(X) () Find P(X2 0.5). expression for fi(x|y); (g) an
The probability density function of X is given by
0 elsewhere
Find the probability density function of Y = X3
f(r)-(62(1-x)for0 < x < 1
2nd pic is answer.
show the work plz
13 Let X and Y have the joint probability density function ,흄.ru2 for 0 < x < y. < 2 f(x,y) = elsewhere What is the joint density function of U it is nonzero? 3X-2Y and V-X + 2Y where 687 Probability and Mathematical Statistics 32768 13° g(u,t) = 0 otherwise.
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
4. Let X and Y have joint density function le-x 0 < y < x < 0 Jxy(x, y) = lo elsewhere Another random variable of interest is U=X–Y. Find the probability density function for U.
) Let X, Y be two random variables with the following
properties. Y had
density function fY (y) = 3y
2
for 0 < y < 1 and zero elsewhere. For 0 < y < 1, given
Y = y, X
had conditional density function fX|Y (x | y) = 2x
y
2 for 0 < x < y and zero elsewhere.
(a) Find the joint density function fX,Y . Be precise about where
the values (x, y) are non-zero....
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
If X and Y have a joint density given by f(x, y)- 2, for 0 < y < x < 1 0, elsewhere (a) If V - -InX, what is the density of V? (b) If V -InX and W X + Y, what is the joint density of V and W? Sketch the region for which the joint density is nonzero
Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
5. If two random variables X and Y have the joint density k(52+2y2) for 0<<2 0 <y< 1 f(r, y) elsewhere (a) Find k (b) Find P(0<x< 1, 0<Y<0.5) (c) Find marginal density fi(a) and f2(y) (d) Are X and Y independent? (e) Find E(X) () Find P(X2 0.5). expression for fi(x|y); (g) an
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