Let $Y$ be the total amount of money paid by any given set of passengers. If there are $X$ passengers in a car, then the driver must pay a toll of $Y=0.5X+3$ .

Then $Y$ has first moment (equal to the mean)

$E[Y]=E[0.5X+3]=0.5E[X]+3E[1]=0.5\mu_X+3=\boxed{4.35}$

and second moment

$E[Y^2]=E[0.25X^2+3X+9]=0.25E[X^2]+3E[X]+9E[1]=0.25E[X^2]+3\mu_X+9$

Recall that the variance is the difference between the first two moments:

$\mathrm{Var}[X]=E[X^2]-E[X]^2\implies E[X^2]={\sigma^2}_X+{\mu_X}^2$

$\implies E[Y^2]=0.25({\sigma^2}_X+{\mu_X}^2)+3\mu_X+9\approx19.22$

$\implies\mathrm{Var}[Y]=E[Y^2]-E[Y]^2=\boxed{0.3}$

3 0

3 years ago

I need the answers please

LekaFEV [45]

all i can really say is it is a y angle

6 0

3 years ago

Please complete the system of equations.

kogti [31]

Answer:

x=-1,y=0

Step-by-step explanation:

-10y+9x=-9

10y+5x=-5

14x=-14

x=-1

-10y-9=-9

y=0

8 0

2 years ago

Which statements are true about the linear inequality y > Three-fourthsx – 2? Select three options.

Vilka [71]

Answer:

Step-by-step explanation:

i) the given linear inequality is $y > \frac{3}{4} x - 2$

ii) the first statement is NOT TRUE. the slope of the is $\frac{3}{4}$ .

iii) the second statement is NOT TRUE. The area above the line is shaded.

iv) the third statement is NOT TRUE. (0,0) is not a solution to the inequality.

v) the fourth statement is TRUE.

5 0

3 years ago

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