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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The random variable x has the following continuous probabil  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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The random variable x has the following continuous probabil [#permalink]
Expert's post 00:00

Question Stats: 12% (01:03) correct 87% (01:12) wrong based on 16 sessions

The random variable x has the following continuous probability distribution in the range 0 ≤ x ≤ $$\sqrt{2}$$, as shown in the coordinate plane with x on the horizontal axis: The probability that x < 0 = the probability that $$x > \sqrt{2} = 0$$.

What is the median of x?

A. $$\frac{\sqrt{2} - 1}{2}$$

B. $$\frac{\sqrt{2}}{4}$$

C. $$\sqrt{2}^-^1$$

D. $$\frac{\sqrt{2} + 1}{4}$$

E. $$\frac{\sqrt{2}}{2}$$
[Reveal] Spoiler: OA

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Re: The random variable x has the following continuous probabil [#permalink]
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Carcass wrote:
The random variable x has the following continuous probability distribution in the range 0 ≤ x ≤ $$\sqrt{2}$$, as shown in the coordinate plane with x on the horizontal axis: The probability that x < 0 = the probability that $$x > \sqrt{2} = 0$$.

What is the median of x?

A. $$\frac{\sqrt{2} - 1}{2}$$

B. $$\frac{\sqrt{2}}{4}$$

C. $$\sqrt{2}^{-1}$$

D. $$\frac{\sqrt{2} + 1}{4}$$

E. $$\frac{\sqrt{2}}{2}$$

$$\sqrt{2}^{-1}$$ and $$\frac{\sqrt{2}}{2}$$ are the same expression. One is the rationalized form of the other. Thus they should be both right.
Founder  Joined: 18 Apr 2015
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Kudos [?]: 1461 , given: 6631

Re: The random variable x has the following continuous probabil [#permalink]
Expert's post
Yes. True. They are equal.

Regards
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Re: The random variable x has the following continuous probabil [#permalink]
Hey Carcass, can you explain the answer to this question? Founder  Joined: 18 Apr 2015
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Re: The random variable x has the following continuous probabil [#permalink]
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Expert's post
Attachment: triangle.jpg [ 28.16 KiB | Viewed 2093 times ]

Actually, the question boils down to this question. which point halves the triangle into to part ?' because the max probability is always 1.

In this case, you have equal probability that x is on the right part of the triangle or in the left.

If the coordinates of C are ($$\sqrt{2}$$, 0 ), then the answer is $$\sqrt{2}$$ minus the only point below this, which means 1.

Hope now is clear.

Regards
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Re: The random variable x has the following continuous probabil [#permalink]
IlCreatore wrote:
Carcass wrote:
The random variable x has the following continuous probability distribution in the range 0 ≤ x ≤ $$\sqrt{2}$$, as shown in the coordinate plane with x on the horizontal axis: The probability that x < 0 = the probability that $$x > \sqrt{2} = 0$$.

What is the median of x?

A. $$\frac{\sqrt{2} - 1}{2}$$

B. $$\frac{\sqrt{2}}{4}$$

C. $$\sqrt{2}^{-1}$$

D. $$\frac{\sqrt{2} + 1}{4}$$

E. $$\frac{\sqrt{2}}{2}$$

$$\sqrt{2}^{-1}$$ and $$\frac{\sqrt{2}}{2}$$ are the same expression. One is the rationalized form of the other. Thus they should be both right.

why not give full explanation? why GMATclub's rules doesnt applied here
Founder  Joined: 18 Apr 2015
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Kudos [?]: 1461 , given: 6631

Re: The random variable x has the following continuous probabil [#permalink]
Expert's post
The same applies here.

Above is a FULL explanation.

The more the questions are tricky the more they boil down in few concepts to solve them.

Do not know why you said that above is not a full explanation  _________________ GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: The random variable x has the following continuous probabil [#permalink]
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Expert's post
A median value of any probability distribution divides the area under the probabaility distribution in two equal parts.

Best understood with following image.

Attachment: Skewed.png [ 131.58 KiB | Viewed 2004 times ]

Now in our case we need to split the triangular distribution along a line $$x=?$$ (parallel to y axis) such that area of the right half is same as the left half.

Area of right half = $$\frac{1}{2} \times$$ Area of the larger triangle.

Now look at the figure below and we have marked out the hight and length of the triangle as x. Now height = length for this triangle because the given line has slope 1.

Attachment: Inkedtriangle_LI.jpg [ 841.95 KiB | Viewed 2003 times ]

Area of right half = $$\frac{1}{2} \times x^2$$= $$\frac{1}{2} \times \frac{1}{2}\times \sqrt{2}^2$$.

Solving for x we get x =1. So median value has to be $$\sqrt{2}-1$$ (refer to the figure above)
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Re: The random variable x has the following continuous probabil [#permalink]
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@Sandy @Carcass can you explain why the smaller triangle is definitively an isosceles triangle? GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: The random variable x has the following continuous probabil [#permalink]
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Expert's post
yashkanoongo wrote:
@Sandy @Carcass can you explain why the smaller triangle is definitively an isosceles triangle?

Because it is given in the question that the slope of the line is 1.

So any triangle made from the line and line parallel to y axis will be an isosceles right triangle.
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Re: The random variable x has the following continuous probabil [#permalink]
sandy wrote:
yashkanoongo wrote:
@Sandy @Carcass can you explain why the smaller triangle is definitively an isosceles triangle?

Because it is given in the question that the slope of the line is 1.

So any triangle made from the line and line parallel to y axis will be an isosceles right triangle.

Thanks for replying man but can you elaborate on your explanation or point me in the direction of a source where I can read up more about this. I dont entirely understand the current explanation. Thanks for the help! GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: The random variable x has the following continuous probabil [#permalink]
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Expert's post
Attachment: InkedInkedtriangle_LI.jpg [ 856.62 KiB | Viewed 1231 times ]

Equation of line making 45 degrees as shown in the figure above is

x+y=100 (say, it can be any number)

what is the value of y at a point x=10?
y=90.

Distance between the point (10,0) and (100, 0) is also 90. This this makes the triangle isosceles. Hope this clears up the doubt.

This is not exactly some concept just basic geometry, so id ont know excatly which resource would be the correct recommendation for this.
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Re: The random variable x has the following continuous probabil [#permalink]
sandy wrote:
Attachment:
InkedInkedtriangle_LI.jpg

Equation of line making 45 degrees as shown in the figure above is

x+y=100 (say, it can be any number)

what is the value of y at a point x=10?
y=90.

Distance between the point (10,0) and (100, 0) is also 90. This this makes the triangle isosceles. Hope this clears up the doubt.

This is not exactly some concept just basic geometry, so id ont know excatly which resource would be the correct recommendation for this.

This definitely clears the doubt, thanks a lot!
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Re: The random variable x has the following continuous probabil [#permalink]
I used an equation of this sort
1/2 * (root(2) - x) * y = x * y + 1/2 * (root(2) - y) * x, provided (x,y) divide the area into two halves
Not sure how to proceed GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: The random variable x has the following continuous probabil [#permalink]
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Expert's post
indiragre18 wrote:
I used an equation of this sort
1/2 * (root(2) - x) * y = x * y + 1/2 * (root(2) - y) * x, provided (x,y) divide the area into two halves
Not sure how to proceed

Get the value of y in terms of x from the equation of the line $$x+y=\sqrt{2}$$. You would get a quadratic equation in x then solve for x.
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Try our free Online GRE Test Re: The random variable x has the following continuous probabil   [#permalink] 19 Nov 2018, 14:21
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