Define the density function (f(x)) as below: f(x) = cx'for 0<x<2,0 otherwise Where c was determined...
Let X1, ... , Xn be a sample from the probability density function f(x0), where 0 € {0,1}. If 0 = 0, then f(20) = ſi if 0<x<1, 10 otherwise, while if @= 1, then fale) - 27if 0<x< 1, 10 otherwise. Find the MLE of 0.
5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O otherwise (c) What is the c.d.f. of Y = X^2 - 1? What is the p.d.f. of Y = X^2 - 1?
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
1. Consider the density f (x) = 0x-1 for 0 < x <1 and 0 otherwise You have data 0.4, 0.6, and 0.8 that is a random sample from this density a. Find the method of moments estimate for 0 b.Find the MLE for 0
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Let the joint density function of random variables X and Y be f(x,y) = 8 - x - y) for 0 < x < 2, 2 < y < 4 0 elsewhere Find : (1) P(X + Y <3) (11) P(Y<3 | X>1) (111) Var(Y | x = 1)
The density of random variable X is f(x) = 5(Xº+1)(3-X) for 1<x<3 and 0 otherwise. Using the R integrate function: 68 a) Find the probability that X > 2.10 b) Find the probability that 1.5 < X < 2.5 c) Find the expected value of x d) Find the standard deviation of X e) In the following paste your R script for this problem
X is a random variable with density function f(x) = x² /3 for -1 < x < 2,0 else. U is uniform(0,1). Find a function g such that g(U) has the same distribution as X.