Question

2

Since X is a continuous random variable, probability of a point is zero and only intervals have non zero probabilities. Therefore

(1) since the support of X will be a subset of R.

(2)

. since probability of a point is zero for continuors random variable.

(3) It may be noted that set of all rational numbers is a countable set.

Therefore

(6)

Given

By definition the distribution function is given by

Since the deinsity function has |x| term we will calculate the distribution function for two ranges separately, that is wehn x<=0 and when x>0.

When x<=0, |x|= - x and

When x>0.

Therefore the distribution function is

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