Consider the following the density function:
f(y) = 4y3 0 < y< 1
0 elsewhere
a) What is the expected value of Y?
b) What is the CDF of Y?
c) What is the probability Y is less than 0.5?
Problem 2: Let Y be the density function given by f(y) = 1.5, -1<y < 0, { 1-cy, 0 <y <1 10, elsewhere. (1) Find the value of c that makes f(y) a density function. (2) Find Fy). (3) Compute Pr(-0.5 <Y <0.5) (4) Graph f(y) and F(y) in the same rectangular coordinate system. (5) Find the expected value u = E[Y]. (6) Find the variance o2 = Var(Y) and the standard deviation o of Y.
Problem 1. Let Y be the density function given by f(y) = 1/5, −1 < y ≤ 0, 1/5 + cy, 0 < y ≤ 1 0, elsewhere. 1. Find the value of c that makes f(y) a density function. 2. Compute the probability P (−1/2 ≤ Y < 1/2) 3. Find the expected value µ and the standard deviation σ of
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2 and f(x.y) = 0 3. otherwise. (a) Show that f(xy) is a density function. (b) Find the probability that both X and Y are less than one. (c) Find the marginal densities of X and Y and show that they are not independent. (d) Find the conditional density of X given Y when Y = 0.5.
Distributions Consider the function f(x)3+1-2-4 0334 (a) Can this function be used as a probability density function? If not, normalize it such that it can, and let that be p(x) (b) Create a CDF of your probability density function, p(x) (c) Compute the expected value and variance of p(z) (d) What is the 90th percentile value of p()
Distributions Consider the function f(x)3+1-2-4 0334 (a) Can this function be used as a probability density function? If not, normalize it such...
# 6 If two random variables have the joint density f(x, y)=59 y?) for 0<x<1, 0<y<1 0 elsewhere a. Find the probability that 0.2 X<0.5 and 0.4<Y<0.6. b. Find the probability distribution function F(x, y). c. Are x and y independent?
Consider the following joint probability density function of the random variables X and Y : 3x−y , 1 < x < 3, 1 < y < 2, f(x, y) = 9 0, elsewhere. (a) Find the marginal density functions of X and Y . (b) Are X and Y independent? (c) Find P(X > 2).
stats
(6) Consider the following joint probability density function of the random variables X and f(x,y) = 9, 1<x<3, 1<y< 2, elsewhere. (a) Find the marginal density functions of X and Y. (b) Are X and Y independent? (c) Find P(X > 2).
1. Consider the following function: 4x 0<x<0.5 f(x)= 4- kx 0.5 <x<1 0 Otherwise a) (5%) Determine k such that f(x) is a probability density function. b) (6%) Determine CDF of x. c) (4%) Using CDE, what is the p(x 0.75) d) (4%) Using CDE what is p(x<0.6) e) (4%) Determine E(x) Type here to search o TT
Let Y have the density function f(y) = ke−2y for all y > 0 and zero everywhere else. Find the value of k that makes f(y) a probability density function. a. Calculate P(0.5 ≤ Y ≤ 1) and P(0.5 ≤ Y < 1). b. Calculate P(0.5 ≤ Y ≤ 1|Y ≤ 0.75) and P(0.5 ≤ Y ≤ 1|Y < 0.75).
The k value that make the following joint density function f(x,y)=kxy, for 0<=x,y<=1 & x+y<=1; =0, elsewhere valid is: