Given a function f(y) {cye-2y, 0<= y < ∞ {0, y<0 Find c that makes f(y) a density function Find P(Y>4) Find the distribution function
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Given a
f(y) {cye-2y, 0<= y < ∞
{0, y<0
- Find c that makes f(y) a density function
- Find P(Y>4)
- Find the distribution function
Step by step
Solved in 5 steps with 4 images
- 62function f (x, y) =15e-2x-3y a joint probability density function over the range 0(i) Continuous RVs X and Y have a joint PDF (m+n+2)! S(x, y) = (1-x)"y". m!n! for 0 < yL The projection X of the radius-vector of a random point on a circumference of radius a onto the diameter has the distribution function (the arcsine law) F(x) { +arcsin for-a< x <6; Determine (a) the probability that X will be on the interval (—a/2, a/2), (b) the quantile x0.75, (c) the probability density f(x) of the random variable X, (d) the mode and median of the distribution.D is defined in the other picture atatchedThe joint probability density of X and Y is f(x, y). Find the marginal density of X at 0.4. The answer should be given to 2 decimal places. g(0.4) = f(x, y)= { 2(x + y) 0A pdf is defined by : f (x, y) = [ C (x + ay) if 0X and Y re random losses with joint density funcTion 2C forocn<00 500000 An Insurance losses pays the total of the twX9 losses to a maximum and oey< lo0, 100 policy on the payment of 100 the expectic fpagment the insurer will make on this policy.Let A > 0. Suppose (X, Y) has joint probability density function given, for all x, y E R, by 3. fx,y(x, y) = { Ay exp(-y(x+ A)), if a 2 0 and y > 0 0, otherwise. (i) Calculate the marginal density of Y. (ii) Let y > 0. Find the the conditional probability density function of X given Y = y. Interpret your answer. (iii) Calculate E[X|Y] and prove that E[X] = +oo. Hint: You can use without a proof that -dy = +oo. %3DThank youThe joint density function is given below; Find the marginal density function for X and Y random variable "check image"#2, Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3. (d) Are X andY independent? Show this in two different ways. (e) Give an integral expression for P(X + 2Y < 1), but do not evaluate it.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON