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Answer:
(a) The value of P (X > 10) is 0.3679.
(b) The value of P (X > 20) is 0.1353.
(c) The value of P (X < 30) is 0.9502.
(d) The value of x is 30.
Step-by-step explanation:
The probability density function of an exponential distribution is:
The value of E (X) is 10.
The parameter λ is:
(a)
Compute the value of P (X > 10) as follows:
Thus, the value of P (X > 10) is 0.3679.
(b)
Compute the value of P (X > 20) as follows:
Thus, the value of P (X > 20) is 0.1353.
(c)
Compute the value of P (X < 30) as follows:
Thus, the value of P (X < 30) is 0.9502.
(d)
It is given that, P (X < x) = 0.95.
Compute the value of <em>x</em> as follows:
Take natural log on both sides.
Thus, the value of x is 30.