Question 1 A continuous random variable X which represents the amount of sugar (in kg) used...
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...
A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function (x)-Ida-92-r) ; otherwise (i)Determine the value of c (ii) Obtain cumulative distribution function. iii) Find P(X 1.2)
A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function (x)-Ida-92-r) ; otherwise (i)Determine the value of c (ii) Obtain cumulative distribution function. iii) Find P(X 1.2)
Question 4 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function (x)-{06r' + 18x-12 ; ishervise : otherwise (iv) Determine the mean and variance of X (v) Determine Var (4X?). Question 5 Consider the following probability distribution for X 30.3 10.2 0.2 0.1 (i) Find E(X). (ii) Find E(2x +4x). (ii) Determine the MGF of X (iv) Calculate Var (X) using MGF ofx Question 6...
Please don’t answer me by hand written.. Would be better if you use your PC to answer so it’s clear for me to read . Thanks ! 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...
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
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.
(e) A continuous random variable X has the probability density function given by: f(x) = ( 2x/√ k for 0 ≤ x ≤ 2 0 otherwise. i. Show that the constant k equals 16. ii. Find the expected value of X. iii. Find the variance of X. iv. Derive the cumulative distribution function, F(x). v. Calculate P(X < 1 | X < 1.5)
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...
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....