Now the PDF of the random variable is
a)For the given random variable ,
The distribution function of is
b)The upper and lower limits of any distribution function is and .
7. Let X be a random variable with distribution function Fx. Let a < b. Consider...
X is a random variable with distribution function Fx, and "a" and "b" are contants, with "a" different from zero and "b" is a real number. Then Y= (aX+b) is also a random variable. (a) Determine the distrbution function Fy as a function of Fx; (b) Assume that X is a continuous random variable with mass probability function fx. Determine the mass probability function fy of Y as a funtion of fx.
Question 3: Let X be a continuous random variable with cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y . Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y
For a random variable X with cumulative distribution function (cdf) Fx(x) = 1- (2/x)^2 ,x>2. (a).Find the pdf fX(x). (b).Consider the random variable Y = X^2. Find the pdf of Y, fY (y).
Proble 2. Let Fx(t) be the cumulative distribution function (CDF) of a continuous random variable X and let Y-X. Express the CDF of Y terms of Fx(t).
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
Problem 4 Let X be a discrete random variable with probability mass function fx(x), and let t be a function. Define Y = t(X): that is, Y is the randon variable obtained by applying the function t to the value of X Transforming a random variable in this way is frequently done in statistics. In what follows, let R(X) denote the possible values of X and let R(Y) denote the possible values of To compute E[Y], we could irst find...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
Let X be a random variable with PDF fx(X). Let Y be a random variable where Y=2|X|. Find the PDF of Y, fy(y) if X is uniformly distributed in the interval [−1, 2]
2) A random variable X has the density function: fr(x) =[u(x-1)-u(x-3)]. Define event B (Xs 2.5) (a) Find the cumulative distribution function, Fy (x). (b) Find the conditional distribution Fx (x|B). the mean E[X], and variance of X Fx(xB)= E[X)= Variance (e) Sketch both Fy(x) and Fx (x|B) on the same plot. Show all important values. (d) Let the output of random variable X above be applied to a square-law device according to Y 5X2. Find the mean value of...
Define a random variable X to be stochastically greater than a random variable Y if FX(t) < Fy(t) for all t and FX(t) < Fy(t) for some t. Let X denote the toss on which the first head appears in repeated tosses of a fair coin, and let y denote the role on which the first 'l' appears in repeated rolls of a fair coin. Which of these two random variables is stochastically greater than the other? (See exercise 1.49...