Question

The probability density shown in Figure 5.21 is the exponential

distribution

f (x) =



0.55 e−0.55x 0 < x

0 elsewhere

Find the probability that

(a) the time to observe a particle is more than

200 microseconds;

(b) the time to observe a particle is less than

Answer 1

$$f(x)= \begin{cases} 0.55e^{-0.55x} &x>0\\ 0 &\text{elsewhere} \end{cases}$$

(a)

$$P(X>200)=1-P(X\le 200)$$

$$=e^{-0.55(200)}\approx0$$

(b)

$$P(X<10)=1-e^{-0.55(10)}\approx0.995913$$