FindCsuch that the following function is a probability
density:
Then compute the second moment ofX, whenXis a random variable having the above PDF. If Y, Z areindependent and having the same PDFf, then write down the joint PDF of(Y, Z).
Homework Answers
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FindCsuch that the following function is a probability
density:
Then compute the second moment ofX, whenXis...
Let Y be a random variable with probability density function, pdf, f(y) = 2e-2y, y >...
Let Y be a random variable with probability density function, pdf, f(y) = 2e-2y, y > 0. Determine f (U), the pdf of U = VY.
A random variable X has the following pdf, where is the parameter, f(x) = x>1. 2+1...
A random variable X has the following pdf, where is the parameter, f(x) = x>1. 2+1 Use the method of transformation to determine the pdf of Y = In X. Identify this distribution. X and Y are random variables with the following joint pdf, f(t,y) = e-(z+y), x >0, y>0. Find the joint probability density function of U and V by considering the transformation U x*y and V = Y. Hence, obtain the marginal density function of U
Find the probability that Y is greater than 3. Let Y have the probability density function...
Find the probability that Y is greater than 3.
Let Y have the probability density function f(y) = 2/y3 if y> 1, f(y) = 0 elsewhere.
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry,...
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry, where 0 < y < z < 2. (a) Find the value of c that makes fx.y (a, y) a valid pdf. (b) Calculate the marginal density functions for X and Y (c) Find the conditional density function of Y X (d) Calculate E(X) and EYIX) (e Show whether X. Y are independent or not.
7. The random variables X and Y have joint probability density function f given by 1...
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1...
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
2. Suppose X and Y are independent random variables with the pdf (probability density func- tion)...
2. Suppose X and Y are independent random variables with the pdf (probability density func- tion) f(x)- for x > 0. (a) What is the joint probability density function of (X, Y)? (b) Define W = X-Y, Z = Y, then what is the joint probability density function fw,z(w, z) for (W, Z). (c) Determine the region for (w, z) where fw,z is positive. (d) Calculate the marginal probability density function for W
I really do need help please 7. X, Y have joint density f(x,y) = 2 if...
I really do need help please
7. X, Y have joint density f(x,y) = 2 if 0 < r <y< 1, S(x, y) = 0 otherwise. Compute the conditional density fxiy
2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1...
2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1 <r< 1 and -1 <y<1, and 0 otherwise. Here is a constant. (a) Determine the value of C. (b) Are X and Y independent? (Explain why or why not.) (c) Calculate the probability that 2X - Y > 0 (d) Calculate the probability that |X+Y| < 2 3. Suppose that X1 and X2 are independent and each is standard uniform on (0,1]. Let Y...
Is a joint density function? If yes, assume it is the joint density function of r.v.s X and Y , and comput...
Is
a joint density function? If yes, assume it is the
joint density function of r.v.s X and Y , and compute the marginal
densities of X and Y .
f(r,y) = { " 0 <y<<11 , otherwise
Let Y be a random variable with probability density function, pdf, f(y) = 2e-2y, y > 0. Determine f (U), the pdf of U = VY.
A random variable X has the following pdf, where is the parameter, f(x) = x>1. 2+1 Use the method of transformation to determine the pdf of Y = In X. Identify this distribution. X and Y are random variables with the following joint pdf, f(t,y) = e-(z+y), x >0, y>0. Find the joint probability density function of U and V by considering the transformation U x*y and V = Y. Hence, obtain the marginal density function of U
Find the probability that Y is greater than 3.
Let Y have the probability density function f(y) = 2/y3 if y> 1, f(y) = 0 elsewhere.
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry, where 0 < y < z < 2. (a) Find the value of c that makes fx.y (a, y) a valid pdf. (b) Calculate the marginal density functions for X and Y (c) Find the conditional density function of Y X (d) Calculate E(X) and EYIX) (e Show whether X. Y are independent or not.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
2. Suppose X and Y are independent random variables with the pdf (probability density func- tion) f(x)- for x > 0. (a) What is the joint probability density function of (X, Y)? (b) Define W = X-Y, Z = Y, then what is the joint probability density function fw,z(w, z) for (W, Z). (c) Determine the region for (w, z) where fw,z is positive. (d) Calculate the marginal probability density function for W
I really do need help please
7. X, Y have joint density f(x,y) = 2 if 0 < r <y< 1, S(x, y) = 0 otherwise. Compute the conditional density fxiy
2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1 <r< 1 and -1 <y<1, and 0 otherwise. Here is a constant. (a) Determine the value of C. (b) Are X and Y independent? (Explain why or why not.) (c) Calculate the probability that 2X - Y > 0 (d) Calculate the probability that |X+Y| < 2 3. Suppose that X1 and X2 are independent and each is standard uniform on (0,1]. Let Y...
Is
a joint density function? If yes, assume it is the
joint density function of r.v.s X and Y , and compute the marginal
densities of X and Y .
f(r,y) = { " 0 <y<<11 , otherwise
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