The given PDF is
a) The probability
The conditional PDF is
b) The conditional CDF is
The conditional CDF is plotted below.
For a continuous variable X with the following PDF: 0sxs2 fx (x) = {2' 0, otherwise...
2. A continuous random variable X has PDF SPI? 1€ (-2,2] fx() = 0 otherwise (a) Find the CDF Fx (x). (b) Suppose 2 =9(X), where gle) = { " Find the (DF, PDF of
Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI <x3) Let X be a continuous random variable with PDF fx(x)- 0 otherwise We know that given Xx, the random variable Y is uniformly distributed on [-x,x. 1. Find the joint PDF fx(x, y) 2. Find fyo). 3. Find P(IYI
Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( ) ?? + 0.4, 0 ≤ ? ≤ 2 0, ??ℎ?????? a. Find the value C that makes fX(x) a valid PDF. (Hint: Draw the PDF to start.) b. Find and sketch the CDF, FX(x). c. Calculate P[X > 1] d. Let A be the event that X > 1. Find and sketch the conditional PDF fX|A(x|A).
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)
4. (20%) Let X be a continuous random variable with the following PDF Sce-4x 0<x fx(x) = to else where c is a positive constant. (a) (5%) Find c. (b) (5%) Find the CDF of X, Fx(x). (c) (5%) Find Prob{2<x<5} (d)(5%) Find E[X], and Var(X).
Let X be a continuous random variable with PDF f(x) = { 3x^3 0<=x<=1 0 otherwise Find CDF of X FInd pdf of Y
1. Let X be a continuous random variable with support (0, 1) and PDF defined by f(x) = ( cxn 0 < x < 1 0 otherwise, for some n > 1. a) Find c in terms of n. b) Derive the CDF FX(x).
(1 point) The pdf of a continuous random variable X is given by 0 otherwise (a) Find E(X). (b) Find Var(X)
3. Consider a continuous random variable X with pdf given by 0, otherwise This is called the exponential distribution with parameter X. (a) Sketch the pdf and show that this is a true pdf by verifying that it integrates to 1 (b) Find P(X < 1) for λ (c) Find P(X > 1.7) for λ : 1
2. A continuous random variable, x, has the following pdf. 0 otherwise Find 110 (a) the mean, (b) the variance