Random variable X has the pdf f(x) = λe^(−λx) for x > 0.
(a) Derive the CDF of X.
(b) Derive the moment generating function of X.
(c) Derive the mean of X.
(d) Derive the variance of X.
Random variable X has the pdf f(x) = λe^(−λx) for x > 0. (a) Derive the...
For the density function f(x) = λe^(-λx) for x>=0, find EX
le* 4. A random variable has a pdf f(x) = lo if x > 0 if xso , find the cdf, mean value and variance. Tel. :
СТ 5. The triangular distribution has pdf 0<<1 f(x) = (2-2) 1<x<2. It is the sum of two independent uniform(0.1) random variables. (a) Find c so that f(x) is a density function. (b) Draw the pdf, and derive the cdf using simple geometry. (c) Derive the cdf from its definition. (d) Derive the mean and variance of a random variable with this distribution.
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
Let X and Y be independent exponential random variables with pdfs f(x) = λe-λx (x > 0) and f(y) = µe-µy (y > 0) respectively. (i) Let Z = min(X, Y ). Find f(z), E(Z), and Var(Z). (ii) Let W = max(X, Y ). Find f(w) (it is not an exponential pdf). (iii) Find E(W) (there are two methods - one does not require further integration). (iv) Find Cov(Z,W). (v) Find Var(W).
Show all work! 0 4.27 The random variable X has CDF: F(x)=Inx 1sxse Determine the mean of X ex 2 1s x o0 4.28 The random variable X has pdf: f(x)={x' 0 otherwise a) Determine the mean of X b) Determine the variance of X 3 1x 4.29 The random variable X has pdf: f(x)= {x4 0 otherwise a) Determine the mean of X b) Determine the variance of X 0<x4 4.30 Determine the mean and variance of X given...
9. Let a random variable X follow the distribution with pdf f(z)=(0 otherwise (a) Find the moment generating function for X (b) Use the moment generating function to find E(X) and Var(X)
Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a random variable X with the CDF given below: 2 F(x)lTe; x20 (a) Plot the CDF by hand. (b) Derive the pdf of this random variable. (c) Compute the P(Xs0.4) 0; x<0 (d) Compute the probability that a randomly selected transistor operates for at least 200 hours. Problem 3: The length of time to failure (in hundreds of hours) for a transistor is a...
Question 6 A random variable X has cdf χ20 Plotthe cdf and identif.,(x)-1-0.2~ a) Plot the cdf and identify the type of the random variable. b) Find the pdf of X. c) Calculate P[-4eX<-1], P(xS2], P(X=1], Pf2-K6], and P[X>10]. d) Calculate the mean and the variance of X. If the random variable X passes through a system with the following chara cteristic function: e) f) Find the pdf of Y. Calculate the mean and the variance of Y. Good Luck
A continuous random variable, X, has a pdf given by f(x) = cx2 , 1 < x < 2, zero otherwise. (a) Find the value of c so that f(x) is a legitimate p.d.f. [Before going on, use your calculator to check your work, by checking that the total area under the curve is 1.] (b) Use the pdf to find the probability that X is greater than 1.5. (c) Find the mean and variance of X. Your work needs...