Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Let $ f(x) = k(3x - x^2) $ if $ 0 \le x \le 3 $ and $ f(x) = 0 $ if $ x < 0 $ or $ x > 3 $.(a) For what value of $ k $ is $ f $ a probability density function?(b) For that value of $ k $, find $ P (X > 1) $.(c) Find the mean.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A. $k=\frac{2}{9}$B. $P(X > 1)=\frac{20}{27}$C. Mean $=\frac{27 k}{4}=\frac{3}{2}$

Calculus 2 / BC

Chapter 8

Further Applications of Integration

Section 5

Probability

Applications of Integration

Missouri State University

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

04:12

Let $f(x)=k\left(3 x-x^{2}…

07:54

01:47

Find the value of $k$ that…

01:13

01:26

Find a value of $k$ that w…

01:06

02:06

The question is there is a function given here like that. If excess between zero and three did a function takes this and otherwise function is there because on it said the request, the function is probably the best function. Pia By the definition off pita I can take the integral off PdF between a m. P. Excuse me, the proto X speed between and and when you replace age mind certainty that baby implemented then it gives me X is between mind 70 for angry and number that stood and is this one in that range is one and this is it goes toe one for NPR Is the future for Pete? Yes, So in the first part it asks for what is K So when you take is integral and take a difficult one and solve it I will replace ethics with our function. But our boundaries has changed with the pantry because when our X is less than zero, our ethics is because zero when our two e's X is greater that tree our function is zero. That means there is no effective integral X is not between geriatric. So this part must be equal to one then I will take that When I take the integral three. X becomes three X square over to and X car becomes X cubed over three and our boundaries Are you time skating? He goes to one. Then I just put three in tow instead of X. This part comes on when I could zero instead of X. This is cereal and there's a minus zero. I didn't write it, so I just calculate nine over to okay, because one that Kay he could still to over. Now this is the first book in the second part off questions it asks for What is a rowboat off X is great man. So I just used the first item here and replace a bit one baby infant When I replace 81 on TV Infinity This part becomes X's great development on poor built off X is greater than man Is Costa integral off ethics between one and infant. I just got here then when I replaced ethics with our function to over nine times three experts X square DX is integral and our boundaries are one tree like previous park. Then I just take integral three x become street external to and expert cups excuse over three on our families here. Then I put three into this part and it becomes one Then I could want instead of X. And this part comes then I just probably. And our boat off X is greater than oneness to end over plants. In the last part, it asks, or what is me off X When I just wantto find me, I just take the intractable X PdF Yes, in general. Then I just apply. When I put X fx, it becomes three x square and minus excuse Then I just take integral aunt to over nine times X coupe minus X for over four and our boundaries our country. And I just put three here on dhe. This part comes when I put zero here instead of X. It is It goes to zero, and I just calculate it is pre or an Army's 3/2

View More Answers From This Book

Find Another Textbook

03:44

The mean cost of a five pound bag of shrimp 50 dollars with standard deviati…

02:18

Question 183 ptsA football team consists of 15 freshmen and 15 sopho…

12:41

Let & = (132)(465) and B (1426)(35)(72) be elements of S,_ Compute fa_ …

06:45

Check my work8 Columbia manufactures bowling balls with a mean weight of…

01:32

A thief steals an ATM card and must randomly guess the correct five-digit pi…

02:44

Given thatL(z) = 2+52is the linearization of a mystery function f(z)…

04:08

Determine the intervals on which the following function is concave up or con…

04:19

Tarif wants to display statistics about tuition payments in the range E3:G12…

03:34

The combination rule takes order into consideration; when determining all po…

03:27

The width of 3 rectangular box is twice the height and the length iS 7 inche…