Question 1 A continuous random variable X which represents the amount of sugar (in kg) used...
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 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)...
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)
Consider the following cumulative distribution function for X. 7 0.1 08 0.9 1.0 Fo) 0.3 0.6 (i) Determine the probability distribution. ii) Find P(X < 1). iii Find P(0 <XS5).
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...
(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)
Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).
13. Let X be a continuous random variable with density P(X0)0.3 and P(X 1) 0.7. Find (i) 1 - Fx(t) where Fx(t) is the cumulative distribution function of X (i) 1-Fx (t) da (iii) 0-P(X = 0) + 1 . P(X = 1) 0
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)