1. Given f(x) = kx(9 - x2)4 0<x<3, otherwise a) Find k. f(x) 20 a pdf pro b) Calculate F(x) and the three quartiles. c) Calculate E(X2) and Var(x2). d) Calculate E(X) and Var(x). (needs more than calc 1) (Bonus)
Consider the following PMF for a continus random variable f(x) = 0,25-Kx®2 Calculate K Calculate P(3<x<5) Calculate P(X <= 4) Calculate E(X) Calculate Var(X)
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
Let pdf of a r.v. X be given by f(x) = 1, 0<x< 1. Find Elet).
For f(x, y) = k(x2 + y2), 0<x< 1 and 0 <y<1 and 0 elsewhere: a) Find k. b) Are X and Y independent? c) Find P(X<0.5, Y>0.5), P( X = 0.5, Y>0.5).
Consider the following PDF for a continus random variable f(x) X: 0 x<0,4 Calculate K Calculate P0, 1<x<0,3) Calculate P(X <= 0,2) Calculate E(X) Calculate Var(X) 3,75-Kx®2]
The density function of X is given by + br if 0 r < 1 f(x) = 0 1 otherwise If E(X) = 3, find a and b. (Hint: Both values are integer.) a = b =
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
2.10.4 Given a function f(x,y) on a compact region E in R^2, Find the maximum and minimum values of f on E, and the points at which these extreme values are attained. f(x, y) = x2 sin y + x, and E is the filled rectangle where -1 < x < 1 and | 0 < a < .
x, 05x<1 if f(x) = {k, 15x<2 where K-3 and F(s) = {{f(x)}, then the value of F(2) rounded to three decimal places is ex X22