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Let X = the time between two successive arrivals at the drive-up window of a local bank. If X has an exponential distribution wi

Illusion [34]

Answer:

(a) $E(X) = 1$

(b) $\sigma_X =1$

(c) P(X ≤ 1) = 0.6321

(d) P(2 ≤ X ≤ 5) = 0.1286

Step-by-step explanation:

From the given information; Let consider X to be the time between two successive arrivals at the drive-up window of a local bank.

However; If X is regarded as the exponential distribution with λ = 1 which is identical to a standard gamma distribution with ∝ = 1

The objective is to compute the following :

(a) The expected time between two successive arrivals is;

$E(X) = \dfrac{1}{\lambda}$

$E(X) = \dfrac{1}{1}$

$E(X) = 1$

(b) The standard deviation of the time between successive arrivals is;

$\sigma_X = \sqrt{\dfrac{1}{\lambda^2}}$

$\sigma_X ={\dfrac{1}{\lambda}}$

$\sigma_X ={\dfrac{1}{1}}$

$\sigma_X =1$

(c) P(X ≤ 1)

P(X ≤ 1) = 1 - e⁻¹

P(X ≤ 1) = 0.6321

(d) P(2 ≤ X ≤ 5)

P(2 ≤ X ≤ 5) = [1 - e⁻⁵] - [1 - e⁻²]

P(2 ≤ X ≤ 5) = 0.9933 - 0.8647

P(2 ≤ X ≤ 5) = 0.1286

7 0

3 years ago

A survey asked 247 students what their favorite subject was. Of those students, there were 115 boys. One hundred two students an

Butoxors [25]

Answer:

Step-by-step explanation:

you have to add a table

6 0

4 years ago

The monomial 36x^4 is a perfect square. What is the square root of 36x^4?

jeyben [28]

Hey there!

$(36x^4)$ squared would equal = 4096.

Your correct answer would be . . .

$\boxed{\boxed{4096}}$

Hope this help you.
~Jay

5 0

4 years ago

Read 2 more answers

Sin^2(x/2)=sin^2x <br> Find the value of x

Veronika [31]

$\sin^2\dfrac x2=\sin^2x$
$\dfrac{1-\cos x}2=1-\cos^2x$
$1-\cos x=2-2\cos^2x$
$2\cos^2x-\cos x-1=0$
$(2\cos x+1)(\cos x-1)=0$
$\implies\begin{cases}2\cos x+1=0\\\cos x-1=0\end{cases}$ $\implies\begin{cases}\cos x=-\frac12\\\cos x=1\end{cases}$

The first case occurs in $0\le x$ for $x=\dfrac{2\pi}3$ and $x=\dfrac{4\pi}3$ . Extending the domain to account for all real $x$ , we have this happening for $x=\dfrac{2\pi}3+2n\pi$ and $\dfrac{4\pi}3+2n\pi$ , where $n\in\mathbb Z$ .

The second case occurs in $0\le x$ when $x=0$ , and extending to all reals we have $x=2n\pi$ for $n\in\mathbb Z$ , i.e. any even multiple of $\pi$ .

6 0

4 years ago

Solve:<br> 13/19- (-1/19)

zhannawk [14.2K]

It’s c I hope it works

6 0

3 years ago

Read 2 more answers