Suppose the pdf of X is f(x)= Ce^(-5x), x > 0 a. What is the value...
1. The joint pdf of (X,Y) is given by f(x,y) = Ce^(-ax - by), 0 0 and b> 0 i) Determine the value of C. ii) Determine correlation between X and Y. iii) Determine the conditional distribution of X, given Y=y. iv) Let Z=XY. Compute E(Z) and Var(Z).
Determine the value of c that makesthe function f(x,y) = ce^(-2x-3y) a joint probability densityfunction over the range 0 < x and 0 < y < x Determine the following : a) P(X < 1,Y < 2) b) P(1 < X < 2) c) P(Y > 3) d) P(X < 2, Y < 2) e) E(X) f) E(Y) g) MARGINAL PROBABILITY DISTRIBUTION OF X h) Conditional probability distribution of Y given that X=1 i) E(Y given X = 1) j)...
Let X be the random variable whose probability density function is f(x) = ce−5x , if x > 0 f(x)=0, if otherwise (a) Find c. (b) Find P(1 ≤ 2X − 1 ≤ 9). (c) Find F(2) where F denotes the c.d.f. of X. (d) Write an equation to find E[3X2 + 15]. You do not have to evaluate it.
4. Suppose that the joint pdf of the random variables X and Y is given by f(x, y) = cx^2 + xy 3 , if 0 < x < 1, 0 < y < 2 0, otherwise. (a) Find the constant value (b) Find the marginal pdf of X. Include the support. (c) Find the conditional density function Y given X = x, i.e., f(y|x) (d) Find the conditional expectation E(Y |X = x). (e) Are X and Y independent?...
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y < 1, y − 1 < x < 1 − y 0 otherwise a) Give an expression for P (X > Y ). b) Find the marginal pdfs for Y . c) Find the conditional pdf of X given Y = y, where 0 < y < 1. d) Give an expression for E[XY ]. e) Are X and Y independent?
3. Let X be a continuous random variable with the following PDF f(x) = ( ke 2 x 20 f(x)= otherwise where k is a positive constant. (a). Find the value of k. (b). Find the 90th percentile of X.
2. Suppose that the continuous random variable X has the pdf f(x) = cx3:0 < x < 2 (a) Find the value of the constant c so that this is a valid pdf. (10 pts) (b) Find P(X -1.5) (5 pts) (c) Find the edf of X use the c that you found in (a). (Hint: it should include three parts: x x < 2, and:2 2) (20 pts) 0,0 <
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
0 〈 y 〈 x2く1· Consider two rvs X and Y with joint pdf f(x,y) = k-y, (a) Sketch the region in two dimensions where fx,y) is positive. Then find the constant k and sketch ) in three imesions Then find the constant k and sketch f(r.y) in three dimensions (b) Find and sketch the marginal pdf fx), the conditional pdf(x1/2) and the conditional cdf FO11/2). Find P(X〈Y! Y〉 1/2), E(XİY=1/2) and E(XIY〉l/2). (c) What is the correlation between X...
Let f(x) = k(5x − x2) if 0 ≤ x ≤ 5 and f(x) = 0 if x < 0 or x > 5. (a) For what value of k is f a probability density function? k = ______ (b) For that value of k, find P(X > 1). P(X > 1) = _______ (c) Find the mean. μ =________ Please show all work neatly, line by line, and justify steps so I can learn. Thank you!