Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x) = 0

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.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Probability and Statistical Inference

ISBN: 978-0321923271

9th edition

Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

See More Books

Question Posted: Oct 12, 2015 08:44 AM

See More Questions

Let f(x, y) be the pdf of the continuous random variable (X, Y). If U = X + Y, then show that the probability density function of U is given by fel")-[fu-v.vd.
Let f: [a, b] x [c, d] R be continuous and suppose D 2 f is continuous. Define f (y) = ba f (x, y) dx. Prove Leibnitz' Rule: f1 (y) = ba D2 f (x, y) dx.
Let f be continuous on a closed, bounded interval [a, b] and suppose that DRf{x) exists for all x (a, b). a) Show that if f(b) < y0 < f(a), then x0 := sup{x [a, b] : f(x) > y0} satisfies f(x0) = y0...
Answer question 43 again for an option with t = .3 years. How does the time until the option expires affect the value of the call option? Question 43 Use the BlackScholes option pricing formula to...
When the observations are large numbers, their final digits are not shown in a stem-and-leaf plot. The plot specifies a leaf unit by which to multiply each observation. For instance, for the cereal...
Air enters a convergent-divergent nozzle at $20 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$ and $40^{\circ} \mathrm{C}$. The receiver pressure is $2 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$...
Name activities in software development covered by various methodologies. Can you explain why more than one methodology is needed in developing a piece of software?
The city of Salinas entered into a contract with Souza & McCue Construction Co. to construct a sewer. City officials knew unusual subsoil conditions (including extensive quicksand) existed that would...
how do you write $ 3 , 4 5 1 in financial notation
Village Hardware is a retail store selling hardware, small appliances, and sporting goods. The business follows a policy of selling all merchandise at exactly twice the amount of its cost to the...
Let the random variable X be equal to the number of days that it takes a high-risk driver to have an accident. Assume that X has an exponential distribution. If P(X < 50) = 0.25, compute P(X > 100 |...
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...
In Exercises 1724,a. List all possible rational roots.b. Use synthetic division to test the possible rational roots and find an actual root.c. Use the quotient from part (b) to find the remaining...
What are the pros and cons of encouraging the development of stock markets in developing countries?
In the text, when we examined statistics from a wide range of developing countries. We found that growth does not guarantee poverty reduction; while higher income is clearly associated with less...
Consider the three recent policy debates concerning microfinance (on subsidies, nonfinancial activities, and commercialization). What kinds of evidence would you seek to resolve these at least in a...
What is meant by financial repression, financial liberalization, currency substitution, and unorganized money markets, and how do they relate to financial policy in developing countries?
What lessons can be learned for low-income countries from the successes of Botswana?
Sketch a graph of the hyperbola. Identify the vertices, foci, and asymptotes. (y + 1) _ (x + 3) 16 9
The manager for retail customers, Katie White, wants to hear your opinion regarding one business offer she has received from an entrepreneur who is starting a mobile phone app called Easy Money. The...
For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that his wife will vote in the referendum is 0.28, and the...
The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.12; the probability that it is a camper is 0.28; and the probability that it is a camper with Canadian...
The probability that the head of a household is home when a telemarketing representative calls is 0.4. Given that the head of the house is home, the probability that goods will be bought from the...
Christopher has collected data about women's heights and their shoe sizes. He noticed that taller women tend to have larger shoe sizes and shorter women tend to have smaller shoe sizes. Christopher...
Discuss the implications of collateral scarcity and collateral velocity for market liquidity and financial stability. How do changes in market conditions, such as regulatory reforms, market...
Critically assess the role of collateral in secured lending and the mitigation of credit risk for lenders. How do banks evaluate the quality, liquidity, and marketability of collateral assets to...

Let F(x) be the cdf of the continuous-type random variable X, and assume that F(x) = 0

Question:

Step by Step Answer:

Let Fx PX x Then PX x y X x PX y 1 Fx y 1 Fx 1 Fy That is with gx ...View the full answer

Probability and Statistical Inference

Students also viewed these Statistics questions