3. (a) Explain why the function f(x) = {*** *8 sin (1) :051 <10 :3€ (-0,...
Determine the value of such that the function f (x, y) = cxy for 0<x<3 and 0 <y<3 satisfies the properties of a joint probability density function. Determine the following. Round your answers to four decimal places (e.g. 98.7654). 1.0994 P&<2,Y<3) 7.4444 P(X<2.0) 21:1878 Pu<Y<1,7) 12489 P(X>1.8,1 <Y<2.5) 7:3733 EX) P(X < 0,8< 4)
help me answer a random variable X has density function f(x) = cx2 for 0<x<3 and f(x) = 0 others. a. Find constant value o b. Find probability P(1 < X<2
X is a random variable with density function f(x) = x² /3 for -1 < x < 2,0 else. U is uniform(0,1). Find a function g such that g(U) has the same distribution as X.
help a random variable X has density function f(x) = cx2 for 0<x<3 and f(x)= 0 others. a. Find constant value o b. Find probability P(1 < X < 2)
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
(1 point) The following density function describes a random variable X F(x) = m if 0 and if 8<x< 16. Draw a graph of the density function and then use it to find the probabilities below A. Find the probability that X lies between 1 and 6. Probability B. Find the probability that X lies between 5 and 10. Probability C. Find the probability that X is less than 9. Probability D. Find the probability that X is greater than...
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.