ft 2 5e2t 5 , 0, t 0 t < 0

Chapter 8, Problem 88

(choose chapter or problem)

Probability A nonnegative function is called a probability density function if

\(\int_{-\infty}^{\infty} f(t) d t=1\).

The probability that lies between a and b is given by

\(P(a \leq x \leq b)=\int_{a}^{b} f(t) d t\).

The expected value of x is given by

\(E(x)=\int_{-\infty}^{\infty} t f(t) d t\).

In Exercises 87 and 88, (a) show that the nonnegative function is a probability density function, (b) find P(0 \leq x \leq 4), and (c) find E(x).

\(f(t)=\left\{\begin{array}{ll}

\frac{2}{5} e^{-2 t / 5}, & t \geq 0 \\

0, & t<0

\end{array}\right.

\)

Text Transcription:

int_-infty^infty f(t) dt=1

P(a leq x leq b)=int_a^b f(t) dt

P(0 leq x leq 4)

f(t)=2/5 e^-2 t / 5, & t geq 0 0, & t<0