If the random variable X is exponentially distributed with parameter $\lambda$ = 1.75, then P(1.5 $\le$ X $\le$3.8), up to 4 decimal places, is:
A) $ 0.0711 . $
B) $ 0.0473 $.
C) $ 0.1184 . $
D) $ 0.4739 $.

Question

If the random variable X is exponentially distributed with parameter $\lambda$ = 1.75, then P(1.5 $\le$ X $\le$3.8), up to 4 decimal places, is: 
A) $ 0.0711 . $
B) $ 0.0473 $.
C) $ 0.1184 . $
D) $ 0.4739 $.

Quizplus · Accepted Answer

The probability density function of an exponential distribution is given by f(x) = $\lambda$e^(- $\lambda$x). So, for $\lambda$ = 1.75, we have f(x) = 1.75e^(-1.75x). The probability of an event is given by the integral of the probability density function over the range of the event. So, P(1.5 $\le$ X $\le$3.8) = $\int_{1.5}^{3.8} 1.75e^(-1.75x) dx$ = -e^(-1.75x) $\bigg|_{1.5}^{3.8}$ = -e^(-6.65) + e^(-2.625) = 0.0711 (rounded to 4 decimal places).

If the Random Variable X Is Exponentially Distributed with Parameter λ\lambdaλ

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