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2 years ago

3

Point \blue{A}Astart color #6495ed, A, end color #6495ed is at \blue{(-1, 8)}(−1,8)start color #6495ed, left parenthesis, minus,

1, comma, 8, right parenthesis, end color #6495ed and point \green{B}Bstart color #28ae7b, B, end color #28ae7b is at \green{(7, 3)}(7,3)start color #28ae7b, left parenthesis, 7, comma, 3, right parenthesis, end color #28ae7b. What is the midpoint of line segment \overline{AB} AB start overline, A, B, end overline?

1 answer:

anzhelika [568]2 years ago

4 0

Answer:

$M = (3,5.5)$

Step-by-step explanation:

Given

$A = (-1,8)$

$B = (7,3)$

Required

Determine the midpoint

This is calculated as thus

$M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where:

$(x_1,y_1) = (-1,8)$

$(x_2,y_2) = (7,3)$

So, we have:

$M = (\frac{-1+7}{2},\frac{8+3}{2})$

$M = (\frac{6}{2},\frac{11}{2})$

$M = (3,5.5)$

Hence;

<em>The midpoint is (3,5.5)</em>

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And p is the success probability.

In counter I :

Y1 ~ Bi (n,p)

Y1 ~ Bi(2,0.2)

$P(Y1=y1)=(2Cy1)(0.2)^{y1}(0.8)^{2-y1}$

With y1 ∈ {0,1,2}

And P( Y1 = y1 ) = 0 with y1 ∉ {0,1,2}

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Y2 ~ Bi (n,p)

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$P(Y2=y2)=(1Cy2)(0.3)^{y2}(0.7)^{1-y2}$

With y2 ∈ {0,1}

And P( Y2 = y2 ) = 0 with y2 ∉ {0,1}

(1Cy2) with y2 = 0 and y2 = 1 is equal to 1 so the probability function for Y2 is :

$P(Y2=y2)=(0.3)^{y2}(0.7)^{1-y2}$

Y1 and Y2 are independent so the joint probability distribution is the product of the Y1 probability function and the Y2 probability function.

$P(Y1=y1,Y2=y2)=P(Y1=y1).P(Y2=y2)$

$P(Y1=y1,Y2=y2)=(2Cy1)(0.2)^{y1}(0.8)^{2-y1}(0.3)^{y2}(0.7)^{1-y2}$

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P( Y1 = y1 , Y2 = y2) = 0 when y1 ∉ {0,1,2} or y2 ∉ {0,1}

b. Not more than one of three customers will spend more than $50 can mathematically be expressed as :

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To calculate $P(Y1+Y2\leq 1)$ we must sume all the probabilities that satisfy the equation :

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