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3 years ago

PLZ PLZ PLZ PLZ PLZ HELP ME!!!10 POINTS AND BRAIMIST IF RIGHT!!!!!

Mathematics

1 answer:

muminat3 years ago

4 0

Answer:

i do not know sorry for that 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]

Y₁ and Y₂ 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(Y₁ > Y₂ | Y₁ < 2 Y₂) = P((Y₁ > Y₂) and (Y₁ < 2 Y₂)) / P(Y₁ < 2 Y₂)

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(Y₁ > Y₂ | Y₁ < 2 Y₂) = (1/6) / (2/3) = 1/4

5 0

2 years ago

Help me with my math question im gonna give you 10 points just to answer that thankkkkkkkkkkkkkkkkkk you

Natalka [10]

Which one you need help with

3 0

3 years ago

In Spetember of 2013, Mario The Baker introduced a new chocolate cake and hired Doug and Jeremy to bake these cakes. Every custo

professor190 [17]

Answer:

There is a 90.32% probability that the cake was baked by Doug.

Step-by-step explanation:

We have these following probabilities:

A 70% probability that Doug bakes the cake.

A 30% probability that Jeremy bakes the cake.

A 40% probability that a cake baked by Doug gets a thumbs up.

A 10% that a cake baked by Jeremy gets a thumbs up.

One cake was selected at random on 10/01/2014 and got a "thumbs up".

1. Find the probability that the cake was baked by Doug.

The probability that a baked cake gets a thumbs up is:

$P = 0.7*0.4 + 0.3*0.10 = 0.31$

Of those, 0.7*0.4 = 0.28 are baked by Doug.

So the probability is:

$P = \frac{0.28}{0.31} = 0.9032$

There is a 90.32% probability that the cake was baked by Doug.

4 0

3 years ago

Can you help me pleaseeeeeew

Lera25 [3.4K]

Answer:

<h2>The answer is A 14.6</h2>

Step-by-step explanation:

the diameter is twice the length of the radius soooo 7.3x2=14.6

making the answer A

4 0

3 years ago

Write a fraction equivalent to 4/18

marysya [2.9K]

Answer:

Its 2/9, sorry I can't show the explanation I have to do my work.

Step-by-step explanation:

6 0

3 years ago

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