The lifetime in months of a transistor in a certain application is random with probability density function:


f(x) = {0.4e^-0.4x, x>0 0, x<0


a. Compute the mean lifetime.

b. Compute the standard deviation of the lifetimes.

c. Compute the cumulative distribution function of the lifetime.

d. Compute the probability that the lifetime will be less than 6 months.

e. Compute the 60^th percentile of the lifetime.

Answers

Answer 1

Answer:

Explained below.

Step-by-step explanation:

The probability density function of lifetime in months of a transistor in a certain application is:

[tex]f(x)=0.4\cdot e^{-0.4x};x>0[/tex]

The probability density function suggests that the random variable X follows a exponential function with parameter λ = 0.4.

(a)

Compute the mean lifetime as follows:

[tex]\mu=\frac{1}{\lambda}=\frac{1}{0.40}=2.5[/tex]

Thus, the mean lifetime is 2.5 months.

(b)

Compute the standard deviation of the lifetimes as follows:

[tex]\sigma=\sqrt{\frac{1}{\lambda^{2}}}=\sqrt{\frac{1}{0.40^{2}}}=2.5[/tex]

Thus, the standard deviation of the lifetimes is 2.5 months.

(c)

The cumulative distribution function of the lifetime is:

[tex]CDF=1-e^{-0.40x}[/tex]

(d)

Compute the probability that the lifetime will be less than 6 months as follows:

[tex]P(X<6)=\int\limits^{6}_{0} {0.40\cdot e^{-0.40x}} \, dx[/tex]

               [tex]=0.40\times [\frac{e^{-0.40x}}{-0.40}]^{6}_{0}\\\\=-1\times [e^{-0.40\times6}-e^{-0.40\times0}]\\\\=-0.090718+1\\\\=0.909282\\\\\approx 0.9093[/tex]

Thus, the probability that the lifetime will be less than 6 months is 0.9093.

(e)

Compute the 60th percentile of the lifetime as follows:

[tex]P(X<x)=0.60\\\\\int\limits^{x}_{0} {0.40\cdot e^{-0.40x}} \, dx=0.60\\\\0.40\times [\frac{e^{-0.40x}}{-0.40}]^{x}_{0}=0.60\\\\-1\times [e^{-0.40\times x}-e^{-0.40\times0}]=0.60\\\\1-e^{-0.40x}=0.60\\\\e^{-0.40x}=0.40\\\\-0.40x=\ln(0.40)\\\\-0.40x=-0.916291\\\\x=2.2907275\\\\x\approx 2.3[/tex]

Thus, the 60th percentile of the lifetime is 2.3 months.


Related Questions

Write the following number in Scientific Notation.
Explain what you did to get your answer
560,000,000,000,000,000

Answers

Answer:

5.6 * 10^17.

Step-by-step explanation:

There are 17 digits after the 5 .

So it's 5.6 * 10^17.

Note that the first number must lie between 1 and 10.

I don't really understand which number we have to write in scientifc notation but I am assuming it is the number 560,000,000,000,000,000.

Ok so, 560,000,000,000,000,000 in scientific notation is 5.6 x 10^17.

This is because if you count the number of spaces behind the decimal point of 5.6 it is equal to 17. So, you would write the answer 5.6 x 10^17.

The lateral surface area of a cube is 400cm². Its total surface area is
_______
a)600cm² b) 2400cm² c) 500cm² d) 650cm²

Answers

Answer:

Step-by-step explanation:

Lateral surface area of cube = 4a²

4a² = 400

   a² = 400÷4

  a² = 100

 a = √100 = √10*10

a = 10 cm

Total surface area = 6a²

                               = 6 * 10²

                               = 6* 100

                               = 600 cm²

Answer:

A

Step-by-step explanation:

I believe that I did this before.

The drama teacher decreased the length of a play from 90 minutes to 60 minutes. What was the percent decrease in the length of the play?

Answers

Answer:

it was decreased by 67%

Step-by-step explanation:

Answer:

67 %

Step-by-step explanation:

Which of the following is the prime factored form of the lowest common denominator of 15/28-5/12?

Answers

Answer:

5/6

Step-by-step explanation:

15/28 - 5/12

LCM of 28 & 12 is 336

420 - 140

--------------

336

=280

--------

336

= 280/336

=5/6

Estimate 4.8 x 4.15.

Answers

Answer:

19.92

Step-by-step explanation:

4.8 x 4.15

Answer:

20 is the correct answer.

Step-by-step explanation:

What is the slope of the line that contains these points?
Pls help

Answers

Answer:

-1

Step-by-step explanation:

m=y2-y1/x2-x1

-6-(-5)=(-1)

6-5=1

-1/1=(-1)

hope this helps :3

if it did pls mark brainliest

Write the expression below as a product of two factors.

12n + 8m - 4

Answers

Answer:

4(2m + 3n - 1)

I hope this helps!

Answer:

12=3*4 or 6*2.   8=4*2  and -4=4*-1

is the factors.

What property justifies 4x=7

Answers

Answer:

x=1.5

Step-by-step explanation:

Answer:

exact form x=7/4

decimal form x=1.75

mixed number form x=1 3/4

Step-by-step explanation:

a line in point-slope form that goes through the points (8,-9) and (-4,15).

Answers

Answer: The answer is 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Identify the domain of the function shown in the graph.
10.
A. 0 B. x < 0
C. x > 0
D. xis all numbers.

Answers

what’s the answer? i’m doing that quiz rn i’m on this question.

The domain of the function shown in the graph is x>0.

What is a function?

A function is the relation between two sets. It relates from the domain set to the range set.

Here, the given graph represents an exponential function starting from (0, 0).

The given graph approaches towards the right along with the x-axis.

Therefore, the initial value of the independent variable in the given function is 0.

Hence, the domain of the given function is x>0.

Learn more about a function here: https://brainly.com/question/4442228

#SPJ2

Bob needs his refrigerator fixed. The repairman will charge Bob a flat fee of $40 plus an additional $15 for each hour he needs to work on it. Write an equation to represent Bob's cost to repair his refrigerator. Use y for the total cost and x for hours.

Answers

Given:

Fixed fee = $40

Additional fee = $15 per hour

To find:

The equation to represent Bob's cost to repair his refrigerator.

Solution:

Let y be the total cost for x hours.

Additional fee for one hour = $15

Additional fee for x hour = $15x

Total cost = Fixed fee + Additional fee

[tex]y=40+15x[/tex]

Therefore, the required equation is [tex]y=40+15x[/tex].

You play basketball At your schools indoor stadium. You have two payment options. Option A is to buy a membership card for $20 and pay $2 each time you go to the gym, t. Option B is to pay $4 each time you go. After how many trips to the gym will the cost be the same?

Answers

Answer:

10 trips

Step-by-step explanation:

Let the number of trips to the gym be represented by t

Option A is to buy a membership card for $20 and pay $2 each time you go to the gym.

$20 + $2× t

20 + 2t

Option B is to pay $4 each time you go.

$4 × t

= 4t

After how many trips to the gym will the cost be the same?

Option A = Option B

20 + 2t = 4t

Collect like terms

20 = 4t - 2t

20 = 2t

t = 20/2

t = 10 trips.

After 10 trips, the gym cost will be the same.

Please find X. I need help!

Answers

There are 2 overlapping triangles here. If the vertical lines are parallel, then these triangles are similar, and corresponding sides occur in a fixed ratio. In particular, we have

2/3 = (2 + x) / (3 + (x + 7))

Solve for x :

2/3 = (2 + x) / (10 + x)

2 (10 + x) = 3 (2 + x)

20 + 2x = 6 + 3x

14 = x

I will give brainliest!!!!!

The school cafeteria is packing picnic baskets for a field trip. To be fair, each basket must have equal numbers of cookies and strawberries for dessert. What is the greatest number of baskets that can be packed with 96 cookies and 88 strawberries?


44

16

32

8

Answers

Answer:

44 because it goes into both of the numbers twice without going over

Step-by-step explanation:

Hope this helps and i am 100% sure it is correct if you are having doubts. Brainliest please

(3-x)3y math homework pleassee help!! Also please include explanation

Answers

Answer:

9y - 3xy

Step-by-step explanation:

3y(3 - x)

Distribute;

3y*3 - 3y*x = 9y - 3xy

i need help with this​

Answers

B is the answer ...............

Answer:

answer is A

Step-by-step explanation:

This symbol is called a tilde. In symbolic logic (a field of math  

used a lot in computer sciences) it is used to denote "not." For  

example, ~A means "not A." In some other contexts, it means  

"approximately." For example, pi ~= 3.1416. (Note that sometimes it is  

written above the equal sign, and sometimes it is used without an  

equal sign - it depends on the situation and the publisher.)

if 3/8 of a pizza cost $5, how much would a full pizza cost? (Be sure to write your answer in the form of money) ​

Answers

$13.35 rougly around that

What do these (>, ≥, <, ≤) mean

Answers

Answer:

Less Than,Less Than or Equal to,Greater Than,Greater Than or Equal to

Step-by-step explanation:

The line under plays the role of an equal sign and the others are pretty self explanatory

Answer: The first one is a greater sign, the second one is greater than or equal to, the third one is less than, and the last one is less than or equal to.

Step-by-step explanation: hope this helps

The equation s =square root 30fd can be used to find the car's speed s in mph given the length d in feet of a skid mark and the friction factor f of the road. Police measured a skid mark of 90 feet on a dry concrete road. If the speed limit is 35mph, was the car speeding? Explain

Answers

Answer:

Yes, the car was speeding the speed limit.

Step-by-step explanation:

The given equation to find the car's speed, s (in mph), is

[tex]s=\sqrt{30fd}[/tex]

where, d is the length of the skid and f is the friction factor.

Police measured a skid mark of 90 feet, so d=90

As the road is dry and of concrete, therefore the friction factor, f=0.8.

So, the speed of the car

[tex]s=\sqrt{30\times0.8\times90} = 46.48[/tex] mph

The speed of the car is 46.48 mph which is more than the speed limit of 35 mph.

Hence, the car was speeding the speed limit.

question.



Contrast the plate movements that cause the stresses in diagrams B and C How did geography affect the way Greeks made their livings?

Answers

Answer:

1. Greece made most of their living from the sea.

2. They became fishers and sailors to get food.

3. On their peninsula they had many different ways to trade with other countries.

4. Greece's mountains aren't good for growing crops, although their climate was mild ,so they could grow wheat, barley, olives, and grapes.

5. Since Greece's sea's are dived from one another, it make trading fiercely independent.1. Greece made most of their living from the sea.

2. They became fishers and sailors to get food.

3. On their peninsula they had many different ways to trade with other countries.

4. Greece's mountains aren't good for growing crops, although their climate was mild ,so they could grow wheat, barley, olives, and grapes.

5. Since Greece's sea's are dived from one another, it make trading fiercely independent.

3. The area of a rectangle is 5/8 square foot. The width of the rectangle is 24
feet. What is the length of the rectangle?
a) 25/16 feet
b) 25/5 feet
c) 14 feet
d) 4 feet

Answers

Answer: 14

Step-by-step explanation:

Well, we know that the formula to fugure out area is :Length times Width

We also know that WIdth is 24. So 24 times __ =5/8.

Now, how do you figure out __? Well, let's first replace that as a variable to make it easier. Let's choose: x   Now, we know that:

x * 24 = 5/8.

To figure out x, we need to do 5/8 divided by 24, right?  When you solve that, the answer would be 15. The closest is 14, so I think the answer is 14.

what is the distance between 1/4 and 3 1/16?

Answers

Answer:

2 13/16

Step-by-step explanation:

3/16 - 1/4

line I is the perpendicular bisector of MN. find m

Answers

Answer:

m = 68

Step-by-step explanation:

MN bisects it or splits it in half so we know N = M, which we could also write as 8x-12 = 5x+18 because they give us those equations

once you have 8x-12 = 5x+18 you can subtract 5x from both sides, so you will get 3x-12 = 18, then you can add 12 to both sides and you will get 3x = 30. Once you have narrowed down to this you can divide three by both sides making x = 10

Now that we know x =10 we can insert it into the equation

5(10) + 18 = m

50 + 18 = m

m = 68

simplify 3+5i/ 6-i!!! Pls help I’m taking a test!!

Answers

Answer:

3 - 0.166666667 i

Step-by-step explanation:

I think this is the answer

I’ll mark brainliest

Evaluate the following expression for

m= -3
N= 4
P= 2

Answers

(4) / (2) + (-3)

4/2 - 3

4/2 - 3/1 ( 3/1 multiply by 2 to make denominators same ok )

4/2 - 6/2

-2/2 ( simplify )

-1 is the answer

Jamal needs to dig a ditch 15 yards long.
Jamal digs 7 yards in the morning and
another 3 yards after lunch. How much is left to dig
more of the ditch is left to dig?

Answers

Answer:

5 yards

Step-by-step explanation:

7y+3y=10yards

15yards-10yards=5yards


When substances go through chemical changes, which of the following will always happen?
OA. One or more substances will be completely destroyed.
OB. Exactly one new substance will form and one will be destroyed.
OC. One or more substances with different chemical properties will form
OD. A gas will form or a white solid will precipitate.

Answers

Answer:

C

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

Just remember this:

Mass can neither be created or destroyed

The radar on a ship picks up two shipwrecks, A and B, 2.5 miles beneath the surface. The distance between the shipwrecks is 0.6 miles. The angle of depression, q, to Shipwreck B depends on the horizontal distance, d, from the ship to Shipwreck A. Write a function for q in terms of d.

Answers

We have
tan 12.5 = 60 / adj rearrange as
adj = 60 / tan 12.5 = about 270.64 m

Using the principle of trigonometry, the angle of depression, q can be expressed in terms of the horizontal distance, d as [tex]q = tan^{-1} [\frac{(d + 0.6)}{2.5}] [/tex]

Using Pythagoras :

SOHCAHTOA

Horizontal distance, d to shipwreck A is added to the distance between shipwrecks A and B to obtain the total horizontal distance

Total horizontal distance = opposite = (d + 0.6) miles

Vertical distance = Adjacent = 2.5 Miles

To obtain the angle of depression, q :

Tanθ = opposite / Adjacent

[tex] tan q = \frac{opposite}{adjacent}= \frac{total \: horizontal \: distance}{height} [/tex]

[tex] tan q = \frac{d + 0.6}{2.5} [/tex]

Therefore, q can be written in terms of d thus ;

[tex]q = tan^{-1} [\frac{(d + 0.6)}{2.5}] [/tex]

Learn more : https://brainly.com/question/17350482

how do you Factor in algebra 2?

for example:
r^2-r-20
and
x^2+8x+12

Answers

(r-5)(r+4)

(x+6)(x+2)

Step-by-step explanation:

1 r^2 - 1 r - 20

multiply the first and third terms

-20 times 1 equals -20. take the -1

*what are two numbers that multiply together that equals -20 but add to equal -1?

-5 times 4 equals -20

-5 plus 4 equals -1

(r-5)(r+4)

1 x^2 + 8 x + 12

multiply the first and third terms

12 times 1 equals 12. take the 8

*what are two numbers that multiply together that equals 12 but add to equal 8?

6 times 2 equals 12

6 plus 2 equals 8

=(x+6)(x+2)

If you teach me how to mark brainlest i will mark you brainlest and you will get 20 points.

Answers

Answer:

tab on it.

Step-by-step explanation:

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