Solution Found!
Let be a continuous rv with cdf [This type of cdf is
Chapter 5, Problem 19E(choose chapter or problem)
Let X be a continuous rv with cdf
\(F(x)=\left\{\begin{array}{cl} 0 & x \leq 0 \\ \frac{x}{4}\left[1+\ln \left(\frac{4}{x}\right)\right] & 0<x \leq 4 \\ 1 & x>4 \end{array}\right.\)
[This type of cdf is suggested in the article “Variability in Measured Bedload-Transport Rates” (Water Resources Bull., 1985: 39–48) as a model for a certain hydrologic variable.] What is
a. \(P(X\ \leq\ 1)\)?
b. \(P((1\ \leq\ X\ \leq\ 3)\)?
c.The pdf of X?
Questions & Answers
QUESTION:
Let X be a continuous rv with cdf
\(F(x)=\left\{\begin{array}{cl} 0 & x \leq 0 \\ \frac{x}{4}\left[1+\ln \left(\frac{4}{x}\right)\right] & 0<x \leq 4 \\ 1 & x>4 \end{array}\right.\)
[This type of cdf is suggested in the article “Variability in Measured Bedload-Transport Rates” (Water Resources Bull., 1985: 39–48) as a model for a certain hydrologic variable.] What is
a. \(P(X\ \leq\ 1)\)?
b. \(P((1\ \leq\ X\ \leq\ 3)\)?
c.The pdf of X?
ANSWER:Answer Step 1 of 5 By using given cdf the respective probabilities are x 0 1 2 3 4 p(x) 0 0.596574 0.25 0.119188 0.034238