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GalinKa [24]
3 years ago
6

Show that p(y) p(y − 1) = (n − y + 1) p yq > 1 if y < (n + 1)p. This establishes that p(y) > p(y − 1) if y is small (y

< (n + 1)p) and p(y) < p(y − 1) if y is large (y > (n + 1) p). Thus, successive binomial probabilities increase for a while and decrease from then on. (n + 1)p > y
Mathematics
1 answer:
horrorfan [7]3 years ago
6 0

Question is not well presented

Consider the binomial distribution with n trials and P(S) = p.

Show that

p(y) /p(y − 1) = (n − y + 1)p /yq > 1 if y < (n + 1)p.

This establishes that p(y) > p(y − 1) if y is small (y < (n + 1)p) and p(y) < p(y − 1) if y is large (y > (n + 1) p). Thus, successive binomial probabilities increase for a while and decrease from then on.

Answer:

See Explanation Below

Step-by-step explanation:

Given that

p(y) /p(y − 1) = (n − y + 1)p /yq > 1 if y < (n + 1)p.

First, we make the following assumption

p(y) /p(y − 1) = (n − y + 1)p /yq = 1;

So, we have

(n − y + 1)p /yq = 1

(n − y + 1)p = yq

Note that p + q = 1;.

So, q = 1 - p

Substitute 1-p for q in the above expression

(n − y + 1)p = y(1-p)

np - py + p = y - py

Solve for y

..... Collect like terms

np + p = y - py + py

np + p = y;

So, y = np + p

y = (n + 1)p

From the above,

We know that

p(y) /p(y − 1) = 1

if y = (n + 1)p.

Similarly, we've also obtain that

p(y) /p(y − 1) > 1 if y < (n + 1)p.

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3 years ago
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X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square
swat32

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = -\frac{4}{5}x+\frac{58}{5}

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

   [x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

   (x + 2)² + (y - 5)²- 29 + 20 = 30

   (x + 2)² + (y - 5)²- 9 = 30

   (x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

    Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

    Slope of the line joining this point to the center (-2, 5),

    m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

          = \frac{10-5}{2+2}

          = \frac{5}{4}

    Let the slope of the tangent which is perpendicular to this line is 'm_{2}'

    Then by the property of perpendicular lines,

          m_{1}\times m_{2}=-1

          \frac{5}{4}\times m_{2}=-1

                 m_{2}=-\frac{4}{5}

   Now the equation of the line passing though (2, 10) having slope m_{2}=-\frac{4}{5}

           y - y' = m_{2}(x-x')

           y - 10 = -\frac{4}{5}(x-2)

           y - 10 = -\frac{4}{5}x+\frac{8}{5}

                  y = -\frac{4}{5}x+\frac{8}{5}+10

                  y = -\frac{4}{5}x+\frac{58}{5}

Therefore, equation of the line will be, y = -\frac{4}{5}x+\frac{58}{5}

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3 years ago
Find the distance between -6 - 8
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Answer:

2

Number line.

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If we start from -6, we will be going __ spaces to the left until we get to -8.

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Answer:

Step-by-step explanation:

Vertex A of the triangle ABC when rotated by 90° counterclockwise about the origin,

Rule to be followed,

A(x, y) → P(-y, x)

Therefore, A(1, 1) → P(-1, 1)

Similarly, B(3, 2) → Q(-2, 3)

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Triangle given in second quadrant will be the triangle PQR.

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Rule to be followed,

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Therefore, triangle given in fourth quadrant is triangle XYZ.

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Answer:

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