What is the constant k that makes the following function a valid pdf?
fX(x) = kx2(1-x)7 for 0 ≤ x ≤ 1, fX(x) = 0 otherwise
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What is the constant k that makes the following function a valid pdf? &nbs
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
1. Determine the constant c such that the given function is a valid joint PDF for the jointly continuous random variables X and Y. f(x,y) ={cry otherwise 0 < y < 2x a. Find the value of the constant c. b. Find the marginal PDFs for X and Y. Are X and Y independent?
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)
please show all work Consider the piece-wise continuous function k(x) as defined below: (Vx+1 k(x) = -* 10 -1<x< 0 0<x51 otherwise a) Find a valid PDF for random variable X, fx(x), that can be derived from k(x), then plot this PDF b) Find and plot the CDF for the random variable X, Fx(x) c) Find the expected value of X, E(X)
3.3. Are the following valid PMFs? If yes, find the constant k that makes it so. a) p(z) (1-2)/k for z = 1,2, , 5 b) p(x)2)/k for 1,2,..,5 뎅 “..
Please answer Problem 18 Problem 17 Find the constant k that makes the following functions PDFs. (a) p(x) = k sin x, 0 < x < a (b) p(x) = kx2(x - 1)2,0 < x < 1 (c) p(x) = kx(1 – x)}, 0 < x < 1 (d) p(x) = k, -1 < x <3 (e) p(x) = kx'e-3, x > 0 Problem 18 For the PDFs in Problem 17, compute the expectations, variances and standard deviations or their...
X and Y are jointly uniformly distributed and their joint PDF is given by: fX,Y(x,y) = {k , 0<=x<=4, 0 <=y <= 8 0 , otherwise } a.) find the value of k that makes the joint PDF valid b.) compute the probability P[(X-2)^2 + (Y-2)^2 < 4] c.) compute the probability P[Y > 0.5X + 5]
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
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...
PLEASE SOLVE FULLY WITH NEAT HANDWRITING AND EXPRESS FINAL ANSWER WITH BOXES!! Suppose that the density (pdf) function for a random variable X is given by fx)or 0s x s2 and fx) 0 otherwise. What is Suppose that the density (pdf) function for a random variable X is given by f(x)--for 0 SX 2 and f(x)-0 otherwise, what is the probability P(0.5 1)? Round your answer to four decimal places. X Suppose that the density (pdf) function for a random...