Question

If x is an exponential variate with mean 5,
evaluate P (0 < x < 1)
A. 0.1813
B. 0.2813
C. 0.3813
D. None of these​

Answer 1

Answer:

none of this is answer

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hope it was helpful

Answer 2

Answer:

Option (D) is the correct answer.

Step-by-step explanation:

Exponential distribution formula:

Continuous random variable X is said to have an exponential distribution, if it has the following probability density function:

$f_X(x| \lambda) = \lambda e^{-\lambda x}$ for $x > 0$ and 0 for $x\leq 0$,

Where λ is the distribution rate.

Mean of exponential distribution,

Mean = $\int\limits^ {\infty}_0 {x \lamda e^{-\lambda x}} \, dx$

         = $\frac{1}{\lambda}$

According to the question,

Mean of exponential variate is 5,

⇒ Mean = 5

⇒ $\frac{1}{\lambda}$ = 5

⇒ $\lambda$ = 1/5

⇒ $\lambda$ = 0.2

Then,

P(0 < X < 1) = $\sum_{x=0}^1 \lambda e^{-\lambda x}$

                  = $0.2 e^{-0.2(0)} +0.2 e^{-0.2(1)}$

Simplify as follows:

P(0 < X < 1) = $0.2 e^{0} +0.2 e^{-0.2}$

                  = $0.2 +0.2(2.71)$ (Since $e^0$ = 1 and $e^{-0.2}$ = 2.71)

                  = 0.2 + 0.542

                  = 0.742

Therefore, option (D) is correct.

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