The function F(x)= x^3/16 - 3*x^4/256 for 0 ≤ x ≤ 4 , 0 for x...
The function F(x)= x^3/16 - 3*x^4/256 for 0 ≤ x ≤ 4 , 0 for x < 0 and 1 for x > 4 is the CDF of a random variable X.
Using R:
a) Using R, create a user-defined function for F in the interval
[0,4].
b) Using this F, find the probability that X < 2.5
c) Using F, find the probability that X > 1.5
d) Using F, find the probability that 1.7 < X < 3.4
e) What is the probability density function(in R code) for X
between 0 and 4 ?
f) Paste your R script in the following box
Homework Answers
ANSWER::
a)
| > fx <- function(x) {x^3/16-3*x^4/256} |
b)
> fx(2.5)
[1] 0.5187988
c)
> fx(4)-fx(1.5)
[1] 0.8483887
d)
> fx(3.4)-fx(1.7)
[1] 0.6812949
e)
fx <- expression(x^3/16-3*x^4/256)
> D(f,'x')
3 * x^2/16 - 3 * (4 * x^3)/256
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