Question: Let f(x) = kx2 (1 x) if 0 < x < 1 and f(x) = 0 if x < 0 or x > 1.

Let f(x) = kx2 (1 – x) if 0 < x < 1 and f(x) = 0 if x < 0 or x > 1.
(a) For what value of k is f a probability density function?
(b) For that value of k, find P(X > ½).
(c) Find the mean.

Step by Step Solution

★★★★★

3.42 Rating (184 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a For 0 x 1 we have fx kx 1x which is nonnegative if and only if k 0 Al... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-I (429).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

For what value of k will the three points (1, 5), (2, 7), and (3, k) be on the same line?

For what value of c does f0 c/e 0.5t dt = 1?

For what value of c does f10 c/x3 dx = 1?

Name Applied Calc. 2 Homework Please show all your work Answers must be supported . Good luck! Due February 28th by 11:59 pm. EST 1. Given y x 3 and y x 2 , find the area between both curves. 2....

Random Variable and its distribution. (a) If the probability of a random variable X is given by f (x) = k(x2 1), x = {1, 2, 3, , 20} then, what is the value of the constant k? (b) Let X1, X2, X3 be...

Problem 1. (1 point) Problem 9. (1 point) Find the general antiderivative for 15 Let f (x) = = x2 + 1' dy = 616 - 413 -4. Enter an antiderivative of f(x) du y = + C. Problem 10. (1 point) Find the...

2 STAT 330: Mathematical Statistics Winter 2016 Assignment 2 Name: ID: Due on Feb 29th (Monday) 11:30am in drop boxes across the hall from MC 4065/4066. 1 1. [7 marks] Let f (x, y) = kxy 2 , if 0 x...

MATH 107 QUIZ 5 NAME: _______________________________ 1. Which of these graphs represent a one-to-one function? (A) (B) (C) (D) 2. The students in history class took a final exam and then took...

1. [1/3 Points] DETAILS PREVIOUS ANSWERS TANAPCALCBR10 2.5.002. MY NOTES ASK YOUR TEA Use the graph of the function f to find the limits at the indicated value of a, if the limit exists. (If an...

Please show your work in details for following question to match with right results indicated in red. c. Where is f increasing and where is f decreasing? ( 4 pts ) Increasing: (- 0o, 0) U (2, 00)...

Production, labour, materials and sales budgets Bullen & Company makes and sells upmarket carry bags for laptop computers. John Crane, controller, is responsible for preparing Bullen's master budget...

Discuss the advantages and disadvantages of regulation (as you see it).

On January 1 . 2 0 2 1 , Riey Corp, acquired some of the outstanding bonds of one of its subaldiwies. The honds had a carrying vatue or 5 7 2 1 , 6 2 0 , and Rliey paid 5 4 0 1 , 9 3 7 for them. How...

A suspension of calcium carbonate particles in water flows through a pipe. Your assignment is to determine both the flow rate and the composition of this slurry. You proceed to collect the stream in...

At a point high in the Earths atmosphere, He 2+ ions in a concentration of 2.8 X 1012/m3 are moving due north at a speed of 2.0 X 105 m/s. Also, a 7.0 X 1011/m3 concentration of O2 ions is moving due...

The coefficients of friction between the three blocks and the horizontal surfaces are ?s = 0.25 and ?k = 0.20. The weights of the blocks are WA = WC = 20 lb, and WB = 10 lb. The velocities of blocks...

The reaction A ? B is carried out in a laboratory reactor. According to a published article the concentration of A should vary with time as follows: C A = C AO exp (? kt) where C AO is the initial...

Company Risk versus Project Risk both Dow chemical Company, a large natural gas user, and Superior Oil, a major natural gas producer, are thinking of investing in natural gas wells near Houston. Both...

Create an equation to convert Fahrenheit degrees into Celsius degrees.

(a) How do you find the distance from a point to a line? (b) How do you find the distance from a point to a plane? (c) How do you find the distance between two lines?

What are the traces of a surface? How do you find them?

Write equations in standard form of the six types of quadric surfaces.

An oil company has a project which requires an investment of $400 million with payoffs depending on the oil price, of $800 million (state 1: high oil price) or $200 million (state 2: low oil price)...

You have $ 1 , 0 0 0 to invest over an investment horizon of three years. The bond market offers various options. You can buy ( i ) a sequence of three one - year bonds; or ( ii ) a three - year...

need help with this problem 14) A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the probability a length is greater than 62 inches