Respuesta :
Answer:
a) 0.3935
a) 0.3935
Memory less property of exponential distribution
Step-by-step explanation:
We are given that X has a exponential distribution.
Thus, it will have a cumulative probability distribution of the form
[tex]P(X \leq x) = 1 - e^{-\lambda x}[/tex], where [tex]\frac{1}{\lambda}[/tex] is the mean of distribution.
We are given [tex]\frac{1}{\lambda} = 10[/tex]
Thus,
[tex]P(X \leq x) = 1 - e^{\frac{-x}{10}}[/tex]
a)[tex]P( x < 5) = 1 - e^{\frac{-5}{10}} = 0.3935[/tex]
b)
[tex]P(x < 15|x > 10) = \displaystyle\frac{P(15 < x < 10)}{P(x > 10)} \\\\= \displaystyle\frac{(1 - e^{\frac{-15}{10} }) - (1 - e^{\frac{-10}{10} }) }{1 - P(x < 10)}\\\\=\displaystyle\frac{(1 - e^{\frac{-15}{10} }) - (1 - e^{\frac{-10}{10} }) }{1 - 1 + e^{\frac{-10}{10} }}\\\\= 0.3935[/tex]
The, answers for a) and b) are same due to memory less property of the exponential distribution.
The future outcomes are not affected by past outcomes.
thus,
[tex]P(X \leq x) = P(x < 15|x > 10)[/tex]
