3. Find the value of ( k ) so that ( f(x)=frac{k}{(x+1)^{2}} ) for ( 2 leq x leq 3 ) is a probability density function.
Added by Allie M.
Close
Step 1
A PDF must satisfy the following conditions: Show more…
Show all steps
Your feedback will help us improve your experience
Hoan Nguyen and 80 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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.
Further Applications of Integration
Probability
Find a value of $k$ that will make $f$ a probability density function on the indicated interval. $$f(x)=k x ;[0,3]$$
Probability and Calculus
Continuous Probability Models
Find $k$ such that each function is a probability density function over the given interval. Then write the probability density function. $$f(x)=k e^{x}, \quad[0,3]$$
Applications of Integration
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD