Suppose That the Random Variable X Has an Exponential Distribution $x$

question 12

Essay

Suppose that the random variable x has an exponential distribution with θ = 3. a. Find the probability that $x$ assumes a value more than three standard deviations from $\mu$ .
b. Find the probability that $x$ assumes a value less than one standard deviation from $\mu$ .
c. Find the probability that $x$ assumes a value within a half standard deviation of $\mu$ .

---

Definitions:

Permutation Test

A nonparametric statistical test method used to determine if two or more samples come from the same distribution.

P-value

A statistical measure indicating the probability of observing test results at least as extreme as those actually observed, assuming that the null hypothesis is true.

Standard Deviation

A measure that indicates the amount of variation or dispersion of a set of values from the mean (average) of that set.

Resamples

The process of taking repeated samples from observed data, often with replacement, to perform statistical inference.