# Question

Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x) = 0 for x ≤ 0 and 0 < F(x) < 1 for 0 < x. Prove that if

P(X > x + y | X > x) = P(X > y),

Then

F(x) = 1 − e−λx, 0 < x.

Which implies that g(x) = acx.

P(X > x + y | X > x) = P(X > y),

Then

F(x) = 1 − e−λx, 0 < x.

Which implies that g(x) = acx.

## Answer to relevant Questions

A certain type of aluminum screen 2 feet in width has, on the average, three flaws in a l00-foot roll. (a) What is the probability that the first 40 feet in a roll contain no flaws? (b) What assumption did you make to solve ...The graphs of the moment-generating functions of three normal distributions—N(0, 1), N(−1, 1), and N(2, 1)—are given in Figure 3.3-3(a). Identify them. A customer buys a $1000 deductible policy on her $31,000 car. The probability of having an accident in which the loss is greater than $1000 is 0.03, and then that loss, as a fraction of the value of the car minus the ...Roll a pair of four-sided dice, one red and one black, each of which has possible outcomes 1, 2, 3, 4 that have equal probabilities. Let X equal the outcome on the red die, and let Y equal the outcome on the black die. (a) ...Let fX(x) = 1/10, x = 0, 1, 2, . . . , 9, and h(y | x) = 1/(10 − x), y = x, x + 1, . . . , 9. Find (a) f(x, y). (b) fY(y). (c) E(Y | x).Post your question

0