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Salsk061 [2.6K]
1 year ago
11

A new cars salesperson, sold an average of $44,531 per day for the first 2 days she worked. The next 11 days she worked, she sol

d an average of $50,063. How much did she sell on average per day over the entire time she worked??
Mathematics
1 answer:
seropon [69]1 year ago
3 0

Given:

First 2 days the salesperson sold an average of $44531 cars.

For next 11 days she sold an average of $50063 cars.

To find the sell on average per day over the entire time,

The total cost is,

2(44531)+11(50063)=639755

The total number of days she work is 2+11=13.

So, the average cost per day is,

a=\frac{639755}{13}=49211.92308

Answer: the average cost per day over entire time salesperson worked is $49211.92

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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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