JaimeBeep
Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

A continuous random variable X has cdf F(x)=x² b (a) Determine the constants a and b. for a < 0, for 0 < x < 1, for x > 1.​

A Continuous Random Variable X Has Cdf Fxx B A Determine The Constants A And B For A Lt 0 For 0 Lt X Lt 1 For X Gt 1 class=

Sagot :

LammettHash

Any proper CDF [tex]F(x)[/tex] has the properties

• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]

• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]

and so

[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]

[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.