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Dmitry [639]
3 years ago
15

Maya shaved her head and then began letting her hair grow. She represents the length \ellℓell of her hair, in centimeters, mmm m

onths after she shaved her head using the equation \ell=1.25mℓ=1.25mell, equals, 1, point, 25, m. What does 1.251.251, point, 25 mean in this situation?
Mathematics
1 answer:
Zarrin [17]3 years ago
4 0

Answer:

Maya's hair grows at the rate of 1.25cm per month

Step-by-step explanation:

After Maya shaved her hair,

She monitored the growth and recorded the length of the hair monthly in centimeters using the equation ell=1.25mℓ=1.25mell

Therefore, since the length of hair is recorded on a monthly basis, 1.25 in the equation refers to the rate of growth as measured by the length of hair per month.

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Answer:

The value of E(Y/X) is 2.

Step-by-step explanation:

As the complete question is not given, thus the complete question is found online and is attached herewith.

So the joint density function is given as

f(x,y)=\left \{ {{\dfrac{x}{8}e^{-\dfrac{x+y}{2}}    \,\,\,\,0 \leq x,0\leq y \atop {0}} \right.

So the marginal function for X is given as

f_x=\int\limits^{\infty}_0 {f(x,y)} \, dy\\f_x=\int\limits^{\infty}_0 \dfrac{x}{8}e^{-\frac{x+y}{2} }dy\\f_x=\int\limits^{\infty}_0 \dfrac{x}{8}e^{-\frac{x}{2}}e^{-\frac{y}{2} }dy\\f_x= \dfrac{x}{8}e^{-\frac{x}{2}}\int\limits^{\infty}_0e^{-\frac{y}{2} }dy\\f_x= \dfrac{x}{4}e^{-\frac{x}{2}}

Now

f(Y/X)=\dfrac{f(X,Y)}{f(X)}\\f(Y/X)=\dfrac{\dfrac{x}{8}e^{-\frac{x+y}{2} }}{\dfrac{x}{4}e^{-\frac{x}{2}}}\\f(Y/X)=\dfrac{1}{2}e^{-\frac{y}{2} }

Now the value of E(Y/X) is given as

E(Y/X)=\int\limits^{\infty}_0 {yf_{Y/X}} \, dy \\E(Y/X)=\int\limits^{\infty}_0 {y\dfrac{1}{2}e^{-\frac{y}{2} } }\, dy\\E(Y/X)=\dfrac{1}{2}\dfrac{\sqrt{2}}{(\dfrac{1}{2})^2}=2

So the value of E(Y/X) is 2.

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Step-by-step explanation:

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