Solution: Here concept of probability density function is used.
Show that the function on the right is a probability density function on [0, 0); then...
Find a value of k that will make fa probability density function on the indicated interval. f(x) = kx, [2, 4] Type an integer or a simplified fraction.)
Q1: Suppose the probability density function of the magnitude X of a bridge (in newtons) is given by fx)-[e(1+3) sxs2 otherwise (a) Find the value of c. (b) Find the mean and variance (c) Find P(1 <x<2.25) (d) Find the cumulative distribution function.
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).
Let X and Y be random variables with joint probability density function f(x, y) = {Cxe for 0 SXS 4,0 s y soo otherwise. Find the marginal probability density function fx(x).
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
Show work. Thanks 2.5.6. The probability density function of a random variable X is given by に " f(x) =10, 0, otherwise (a) Find c. (b) Find the distribution function F(x) (c) Compute P 3)
Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x) = kx2; (-1,4] Å f(x 1 / 2 (x) = 1 x ² O 3 64 7; f(x) = CS x2 2. 65
7. Show that if the joint probability density function of X and Y is if 0 < x <.. =sin(x + y) f(x, y) = { VI fres 9 Line + »» Hosszž, osys elsewhere, then there exists no linear relation between X and Y.
Compute the right-hand and left-hand derivatives as limits and check whether the function is differentiable at the point P. What is the right-hand derivative of the given function? f(4 +h)-f(4) lim h =17 no (Type an integer or a simplified fraction.) What is the left-hand derivative of the given function? y=(x-4)2 - 4 lim f(4 + h) – f(4) . n0 (Type an integer or a simplified fraction.) Is the given function differentiable at the point P? P(4,-4) Yes Νο...