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3 years ago

5

Suppose that the gas tank of a car holds 12 gallons , and that the car uses 1/20 of a gallon per mile . Let x be the number the

car has gone since the tank was filled

1 answer:

777dan777 [17]3 years ago

6 0

Answer:

I really dont Know

Step-by-step explanation:

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Let Y1 and Y2 be independent exponentially distributed random variables, each with mean 7. Find P(Y1 > Y2 | Y1 < 2Y2). (En

ArbitrLikvidat [17]

<em>Y</em>₁ and <em>Y</em>₂ are independent, so their joint density is

$f_{Y_1,Y_2}(y_1,y_2)=f_{Y_1}(y_1)f_{Y_2}(y_2)=\begin{cases}\frac1{49}e^{-\frac{y_1+y_2}7}&\text{for }y_1\ge0,y_2\ge0\\0&\text{otherwise}\end{cases}$

By definition of conditional probability,

P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = P((<em>Y</em>₁ > <em>Y</em>₂) and (<em>Y</em>₁ < 2 <em>Y</em>₂)) / P(<em>Y</em>₁ < 2 <em>Y</em>₂)

Use the joint density to compute the component probabilities:

• numerator:

$P((Y_1>Y_2)\text{ and }(Y_1$

$=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1$

$=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1$

$=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty$

$=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16$

• denominator:

$P(Y_1$

(I leave the details of the second integral to you)

Then you should end up with

P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = (1/6) / (2/3) = 1/4

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3 years ago

Kaitlin has been given a list of bands and asked to place a vote. Her vote must have the names of her favorite and second favori

umka2103 [35]

Complete question :

Kaitlin has been given a list of 5 bands and asked to place a vote. Her vote must have the names of her favorite and second favorite bands from the list. How many different votes are possible?

Answer:

20 different votes

Step-by-step explanation:

Total number of bands = 5

To select her favorite ; she chooses 1 from the five ;

Number of bands left = 4

From. The 4 she chooses one ; which is her second favorite

Number of different votes possible :

Favorite selection * second favorite selection

(5 * 4) = 20 different votes.

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3 years ago

Solve x^2+20x+100=50

uysha [10]

1. You con solve the quadratic equation x^2+20x+100=50<span> by following the proccedure below:

2. Pass the number 50 from the right member to the left member. Then you obtain:

x^2+20x+100-50=0
</span><span> x^2+20x+50=0
</span><span>
3. Then, you must apply the quadratic equation, which is:

x=(-b±√(b^2-4ac))/2a

</span><span>x^2+20x+50=0
</span><span>
a=1
b=20
c=50

4. Therefore, when you substitute the values into the quadratic equation and simplify ir, you obtain that the result is:

-10</span>±5√2 (It is the last option).

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Alice waters her plants every 2 days

snow_lady [41]

What is the question?

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Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest deg

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Heyyyyyy new friends and I have no clue what the answer is cause I don’t feel like reading that but anyway yea nfs?

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