The function F(x)=1cos(x)

2

for 0x

, 0 for x< 0 and 1 for x>is the CDF of a random variable X.

Using R:

a) Using R, create a user-defined function for F(named F) in the interval [0,].

b) Using this F, find the probability that X > 1.5

c) Using F, find the probability that X < 1.5

d) Using F, find the probability that 0.5 < X < 1.4

e) What is the probability density function(in R code) for X between 0 and?

f) Paste your R script in the following box