GATE Overflow Test Series | Probability | Test 1 | Question: 18

Question

Assume that a cricket ball lasts on average 100 overs. Assuming exponential distribution, the absolute value of the difference in probability that it lasts more than $150$ overs and the probability that it lasts less than $80$ overs is ____ (correct up to 2 decimal points)

Answer 1

$\lambda = \dfrac{1}{100}.$

$P(X\geq150) = e^{-\lambda 150} = e^{-1.5} =0.2231  $

$P(X<80) = 1 - P(X\geq 80) = 1 - e^{-80\lambda} = e^{-0.8} =0.5506 $

So, difference in probabilities $=0.3275$

Comments

For exponential distribution,

$E(x)=1/\lambda=100$

$P(X\geqslant 150)= \int_{150}^{\infty }\lambda e^{-\lambda x}$dx

$P(X< 80)= \int_{-\infty}^{80}\lambda e^{-\lambda x}dx\equiv \int_{0}^{80}\lambda e^{-\lambda x}dx$

Answer 2

.