13. Let X be a continuous random variable with density P(X0)0.3 and P(X 1) 0.7. Find...
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
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
please answer question 22
* 33 334 22. Let Xi and X, are continuous random variable with densities f(x) = 1 SIS2 and (0, Otherwise 9(3) 22 a respectively, where a, b > 0 are constants. 10, Otherwise (i) Find the cumulative distribution function Fx:(t) of X. (ll) Find the cumulative distribution function Fx.(t) of Xy. Your answer may involve a, b. (iii) Find the 50th percentile of X,. (iv) Find a ondo such that X; and Xhave the same...
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.
1. Let X be a continuous random variable with the probability density function fx(x) = 0 35x57, zero elsewhere. Let Y be a Uniform (3, 7) random variable. Suppose that X and Y are independent. Find the probability distribution of W = X+Y.
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-102-x) 1sxs2 ; otherwise (0) (ii) (ii) Determine the value of c. Obtain cumulative distribution function Find P(X < 1.2). Consider the following cumulative distribution function for X. 06 0.8 1.0 Fx) 0.9 (i) Determine the probability distribution. (ii) Find P(X 1). (ii) Find P(OX5) Question 3 Consider the following pdf otherwise (i) (ii)...
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-1(2-xsxs2 ; otherwise f(x) (i) Determine the value of c ii) Obtain cumulative distribution function (iii) Find P(X<1.2). Question 2 Consider the following cumulative distribution function for X 0.3 0.6 0.8 0.9 1.0 (i) Determine the probability distribution. ii) Find P(X<1). iii Find P(O <Xs5). Consider the following pdf ,f(x) = 2k ; 1<x<2...