5^4-x^2+x-2 divided by x

Our faucet is broken, and a plumber has been called. The arrival time of the plumber is uniformly distributed between 1pm and 7p

Ymorist [56]

Answer:

$E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours$

$Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2$

Step-by-step explanation:

Let A the random variable that represent "The arrival time of the plumber ". And we know that the distribution of A is given by:

$A\sim Uniform(1 ,7)$

And let B the random variable that represent "The time required to fix the broken faucet". And we know the distribution of B, given by:

$B\sim Exp(\lambda=\frac{1}{30 min})$

Supposing that the two times are independent, find the expected value and the variance of the time at which the plumber completes the project.

So we are interested on the expected value of A+B, like this

$E(A +B)$

Since the two random variables are assumed independent, then we have this

$E(A+B) = E(A)+E(B)$

So we can find the individual expected values for each distribution and then we can add it.

For ths uniform distribution the expected value is given by $E(X) =\frac{a+b}{2}$ where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:

$E(A)=\frac{1+7}{2}=4 hours$

The expected value for the exponential distirbution is given by :

$E(X)= \int_{0}^\infty x \lambda e^{-\lambda x} dx$

If we use the substitution $y=\lambda x$ we have this:

$E(X)=\frac{1}{\lambda} \int_{0}^\infty y e^{-\lambda y} dy =\frac{1}{\lambda}$

Where X represent the random variable and $\lambda$ the parameter. If we apply this formula to our case we got:

$E(B) =\frac{1}{\lambda}=\frac{1}{\frac{1}{30}}=30min$

We can convert this into hours and we got E(B) =0.5 hours, and then we can find:

$E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours$

And in order to find the variance for the random variable A+B we can find the individual variances:

$Var(A)= \frac{(b-a)^2}{12}=\frac{(7-1)^2}{12}=3 hours^2$

$Var(B) =\frac{1}{\lambda^2}=\frac{1}{(\frac{1}{30})^2}=900 min^2 x\frac{1hr^2}{3600 min^2}=0.25 hours^2$

We have the following property:

$Var(X+Y)= Var(X)+Var(Y) +2 Cov(X,Y)$

Since we have independnet variable the Cov(A,B)=0, so then:

$Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2$

3 0

3 years ago

1 1 2 4 3 9 4 what is the next number

Alina [70]

The answer is 16. 1^2 is 1, 2^2 is 4, 3^2 is 9, and 4^2 would be 16.

3 0

3 years ago

Absolote value x=6. any help

loris [4]

I can help but what is the q it doesn’t make since

7 0

3 years ago

47% of $118 estimated

bezimeni [28]

1. We assume, that the number 118 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for. 
3. If 118 is 100%, so we can write it down as 118=100%. 
4. We know, that x is 47% of the output value, so we can write it down as x=47%. 
5. Now we have two simple equations:
1) 118=100%
2) x=47%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
118/x=100%/47%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 47% of 118

118/x=100/47
(118/x)*x=(100/47)*x - we multiply both sides of the equation by x
118=2.12765957447*x - we divide both sides of the equation by (2.12765957447) to get x
118/2.12765957447=x 
55.46=x 
x=55.46

now we have: 
47% of 118=55.46

6 0

3 years ago

Read 2 more answers

Explain how you should use the formula to calculate the number of pennies on Rows 1-4. Why use the formula?

tigry1 [53]

Answer:

The formula is much faster.

Substitute in a1=1, r = 2, and n = 32 into the formula.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

5^4-x^2+x-2 divided by x - 2