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An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft3, and 20 ft3. Let X = the ra

ruslelena [56]

Answer:

$E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6$

$E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6=349.2$

$V(X) = E(X^2)-[E(X)]^2=349.2-(18.6)^2=3.24$

The expected price paid by the next customer to buy a freezer is $466

Step-by-step explanation:

From the information given we know the probability mass function (pmf) of random variable X.

$\left|\begin{array}{c|ccc}x&16&18&20\\p(x)&0.3&0.1&0.6\end{array}\right|$

Point a:

The Expected value or the mean value of X with set of possible values D, denoted by E(X) or μ is

$E(X) = $\sum_{x\in D} x\cdot p(x)$

Therefore

$E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6$

If the random variable X has a set of possible values D and a probability mass function, then the expected value of any function h(X), denoted by E[h(X)] is computed by

$E[h(X)] = $\sum_{D} h(x)\cdot p(x)$

So $h(X) = X^2$ and

$E[h(X)] = $\sum_{D} h(x)\cdot p(x)\\E[X^2]=$\sum_{D}x^2\cdot p(x)\\ E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6\\E(X^2)=349.2$

The variance of X, denoted by V(X), is

$V(X) = $\sum_{D}E[(X-\mu)^2]=E(X^2)-[E(X)]^2$

Therefore

$V(X) = E(X^2)-[E(X)]^2\\V(X)=349.2-(18.6)^2\\V(X)=3.24$

Point b:

We know that the price of a freezer having capacity X is 60X − 650, to find the expected price paid by the next customer to buy a freezer you need to:

From the rules of expected value this proposition is true:

$E(aX+b)=a\cdot E(x)+b$

We have a = 60, b = -650, and E(X) = 18.6. Therefore

The expected price paid by the next customer is

$60\cdot E(X)-650=60\cdot 18.6-650=466$

4 0

2 years ago

A farmer has 300 ft of fencing with which to enclose a rectangular pen next to a barn. The barn itself will be used as one of th

Katarina [22]

Let x represent the length of the side of the pen that is parallel to the barn. Then the area (y) will be
.. y = x(300 -x)/2
This describes a downward opening parabola with zeros at x=0 and x=300. The vertex (maximum) will be found at the value of x that is halfway between those, x = 150.

For that value of x, the pen area is
.. y = 150(300 -150)/2 = 150^2/2 = 11,250 . . . . . square feet.

5 0

2 years ago

Which of the following stocks had the biggest increase in price from the previous day

SCORPION-xisa [38]

Answer:

Step-by-step explanation:

Without any calculations, you can eliminate Apple and Google: both of them suffered looses. Neither went up. They went down. eBay went up ever so slightly (0.09 on nearly 21 dollars). At least it did not loose money on the day. So it is possible.

Netflix went up $2.73 on a stock that was about 118 on it's close. So while ebay only made $.09, Netflix was the winner on the day both in absolute and % terms.

4 0

2 years ago

Read 2 more answers

Work out the height of this triangle with base, b= 7.7mm and area,A=210.21mm

iris [78.8K]

Answer:

h = 27.3

Step-by-step explanation:

A = bh

h = A/b

h = 210.21 / 7.7

h = 27.3

8 0

1 year ago

On a coordinate plane, a curved line begins at point (negative 2, negative 3), crosses the y-axis at (0, negative .25), and the

shepuryov [24]

Answer:

Option D

Step-by-step explanation:

correct answer on edge :)

7 0

2 years ago