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PIT_PIT [208]
2 years ago
7

Let x and y be independent each uniformly distributed on {1,2,...,n} find p(x < y )

Mathematics
1 answer:
bulgar [2K]2 years ago
8 0
If we draw the contingency table of x (vertical) against y (horiz.), we have a square.
For n=4, we have   (legend:  < : x<y   = : x=y   > : x>y

y      1  2  3  4
x
1      = <  <  <
2      > =  <  < 
3      >  >  = <
4      >  >  >  =

We see that there are n(n-1)/2 cases of x<y out of n^2.
Therefore, 
p(x<y)=n(n-1)/(2n^2)=(n-1)/(2n)

However, if the sample space is continuous, it will be simply p(x<y)=1/2.

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Zarrin [17]

Answer:

Angles A and E are congruent.

Step-by-step explanation:

Angles A and E are congruent because they are alternate interior angles.

8 0
2 years ago
Write an equation for the translation of x^2 + y^2 = 49 by 7 units right and 4 units up
Tatiana [17]

Answer:

(x - 7)² + (y - 4)² = 49

Step-by-step explanation:

Given

Equation: x² + y² = 49

Required:

New Equation when translated 7 units right and 4 units up

Taking it one step at a time.

When the equation is translated 7 units right, this implies a negative unit along the x axis.

The equation becomes

(x - 7)² + y² = 49

When the equation is translated 4 units up, this implies a negative unit along the y axis.

(x - 7)² + (y - 4)² = 49

The expression can be further simplified but it's best left in the form of

(x - 7)² + (y - 4)² = 49

8 0
2 years ago
How do i check 1/3v=-5 ?
BigorU [14]

If you mean that you want to solve the equation for v, then all you need to do is to multiply both sides by 3:

\dfrac{1}{3}v=-5 \iff 3\cdot \dfrac{1}{3}v = -5\cdot 3 \iff v=-15

4 0
3 years ago
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inc
Elan Coil [88]
\sf Cylinder ~volume = \pi r^2 h \\  \\ v = \pi (4)^2(9) \\  \\ v=\pi (16)(9) \\  \\ v=144 \pi  \\ v=452.16\\  \\  \\ Cone~volume = \frac{1}{3} \pi r^2 h \\  \\ v =  \frac{1}{3} \pi (4)^2 (18) \\  \\ v=96 \pi \\ v=301.44 \\  \\  \\ The~ volume ~of ~a ~cylinder ~is~ 1.5~ times~ more ~than ~the ~volume ~of~a~cone.
4 0
3 years ago
If the area of the rectangle is equal 48, what is the value of x? Write an equation you can use to solve.
schepotkina [342]

6 \times 8 = 48

hope it is correct if not I'm sorry

3 0
3 years ago
Read 2 more answers
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