Please assist with all questions and add R script as well. **Understanding and Implementing Cumulative Distribution Function (CDF) in R**The function \( F(x) = \frac{1}{32}(6 - x) \cdot x^2 \) for \( 0 \leq x \leq 4 \) and \( 0 \) for \( x < 0 \) and \( 1 \) for \( x > 4 \) is the cumulative distribution function (CDF) of a random variable \( X \).**Using R:****a) Using R, create a user-defined function for \( F \) (named F) in the interval \([0, 4]\).**```RF <- function(x) { if(x < 0) return(0) if(x > 4) return(1) return((1/32) * (6 - x) * x^2)}```**b) Using this \( F \), find the probability that \( X < 2.3 \).**```Rprob_X_less_than_2_3 <- F(2.3)print(prob_X_less_than_2_3)```**c) Using \( F \), find the probability that \( X > 3.7 \).**```Rprob_X_greater_than_3_7 <- 1 - F(3.7)print(prob_X_greater_than_3_7)```**d) Using \( F \), find the probability that \( 2.3 < X < 3.7 \).**```Rprob_X_between_2_3_and_3_7 <- F(3.7) - F(2.3)print(prob_X_between_2_3_and_3_7)```**e) What is the probability density function (in R code) for \( X \) between 0 and 4?**```Rf <- function(x) { if(x < 0 || x > 4) return(0) return((1/16) * x * (3 - x))}```**f) Paste your R script in the following box**```RF <- function(x) { if(x < 0) return(0) if(x > 4) return(1) return((1/32) * (6 - x) * x^ ### Probability Density Function and ComputationsThe probability density function of random variable \( X \) is given by:\[ f(x) = \frac{3}{500}(10x - x^2) \quad \text{for} \quad 0 \leq x \leq 10 \quad \text{and} \quad 0 \quad \text{otherwise.} \]Perform the following computations using the R `integrate` function:#### a) Find the probability that \( X > 6 \)\[ \boxed{ }\]#### b) Find the probability that \( 3 < X < 7 \)\[ \boxed{ }\]#### c) Find the expected value of \( X \)\[ \boxed{ }\]#### d) Find the variance of \( X \)\[ \boxed{ }\]#### e) Find the standard deviation of \( X \)\[ \boxed{ }\]#### f) Find the probability that \( X \) is within 0.50 standard deviations of its expected value\[ \boxed{ }\]#### g) In the following paste your R script for this problem```R# Your R script here```

given the cumulative density Function a) creating user defined function for F in the interval [0,4]…

The function F(x)= Using R: a) Using R, create a user-defined function for F (named F) in the interval [0,4]. b) Using this F, find the probability that X < 2.3 | c) Using F, find the probability that X > 3.7| d) Using F, find the probability that 2.3 < X < 3.7 32 (6-x).x² for 0 ≤x ≤4 and 0 for x<0 and 1 for x > 4 is the CDF of a random variable X. e) What is the probability density function(in R code) for X between 0 and 4 ?

The function F(x)= Using R: a) Using R, create a user-defined function for F (named F) in the interval [0,4]. b) Using this F, find the probability that X < 2.3 | c) Using F, find the probability that X > 3.7| d) Using F, find the probability that 2.3 < X < 3.7 32 (6-x).x² for 0 ≤x ≤4 and 0 for x<0 and 1 for x > 4 is the CDF of a random variable X. e) What is the probability density function(in R code) for X between 0 and 4 ?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Golden section unimodal function
Var(Z)=(10)E(Z) Find the distribution of Z and find its parameter(s)
Using linear approximation to estimate f(3.2)-f(3) for f(x)8/(1+x^2)
Find the value or values of c that satisfy the equation f(b) - f(a) b-a 1x)-4x²+4x-3, 1-2,0 f(b) - f(a) The value(s) of c that satisfy the equation = f'(c) is/are b-a f'(c) in the conclusion of the Mean Value Theorem for the following function and interval. (Type a simplified fraction. Use a comma to separate answers as needed.)
Income_(Y) Money_Supply_(X)116,652 42,011120,392 43,313124,572 44,808132,624 48,056139,656 50,094144,752 52,117150,164 54,253153,560. 56,512157,328 59,243161,740. 60,783168,732 64,782180,002 66,338182,744 68,694190,172 72,238191,592 74,544195,600 77,300201,204 80,021204,160 83,482207,827 85,868214,712 87,911
Minimize and maximize the function f(x)=(3x^2+3x)/(3x^2+1)
x2+2x+3 -dx (x-6)(x²+4) Evaluate / Files
multivariate calculus Partially differentiate the follwoing with respect to x1 and x2
Find the value or values of c that satisfy the equation f(x) = 2x² + 5x - 3, [-1,2] f(b)-f(a) b-a = f'(c) in the conclusion of the Mean Value Theorem for the following function and interval. The value(s) of c that satisfy the equation f(b)-f(a) b-a = f'(c) is/are (Type a simplified fraction. Use a comma to separate answers as needed.)
Midline theorem
Measuring permeability for reservoir formations has shown that permeability is having f(x) - (100e ")/(3x-2) where 35SXS5 D Determine the probability of permeability to be greater than or equal to 3 uD and less than 4 uD.
Question 10 2r+5 Find the RANGE of the function f(x) = Section 4.2 O y + 3 O y + 1 O + 3 O y # -1 O + 1 O + -1 « Previous Not saved Jquizzes/3042240/take/questions/55226791