Consider the following exponential probability density function. 1-x/5 f(x) for x 20 (a) Write the formula for P(x S x). (b) Find P(x s 3). (Round your answer to four decimal places.) (c) Find P(x 2 5). (Round your answer to four decimal places.) (d) Find P(x s 7). (Round your answer to four decimal places.) (e) Find P(3 sxs 7). (Round your answer to four decimal places.)

Determine the probability density function for the following cumulative distribution function. 0 x < 0 0.2x 0 < x < 4 4 < x < 9 9 ≤ x F(x) = 0.04x +0.64 1 Find the value of the probability density function at x = 3.

Solve it

Consider the following exponential probability density function. 1 -x/4 f(x) = -e (a) Write the formula for P(x ≤ xo). for x ≥ 0 (b) Find P(x ≤ 2). (Round your answer to four decimal places.) (c) Find P(x ≥ 4). (Round your answer to four decimal places.) 0.3679 (d) Find P(x ≤ 5). (Round your answer to four decimal places.) (e) Find P(2 ≤ x ≤ 5). (Round your answer to four decimal places.)

The life X (in hours) of a battery in constant use is an arbitrary variable with exponential density. What is the probability that the battery will last more than 28 hours if the average life is 8 hours? (Give your answer to four decimal places.) P≈

Recall that the exponential probability density function is defined as 1 f(x) = — - e-2/A. е Suppose that the lifetime in hours of a certain lightbulb is exponential distributed with λ = 3000. Find the probability that a given lightbulb will last more than 7300 hours. P(X> 7300)