A gardener uses 1\3 of liter of water to water 2\7 of the garden

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

3 years ago

The length of a ribbon is 3/4 meters. Sun hi needs pieces measuring 1/3 meter. What are the greatest number of pieces measuring

Llana [10]

2, since 2x 1/3 is 2/3, which is less than 3/4.

5 0

3 years ago

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1. Solve & Graph -5 ¾+3h≤ 9 ¼1.

Dennis_Churaev [7]

Answer:

h≤ 2423/492

Step-by-step explanation

3h+ −23/4 ≤ 370/41

3h + −23/4 + 24/4 ≤ 370/41 + 23/4

3h ≤ 2423/164

3h 3 ≤ 2423/164/3

h ≤ 2423/492

Step 1: Add 23/4 to both sides.

Step 2: Divide both sides by 3.

8 0

3 years ago

How can I make 8 and 62/40 a proper mixed number

Lina20 [59]

You can't make it proper.You can only simplify.
Step 1: Factor both the numerator and denominator down to prime factors:62 = 2 * 31 
40 = 23 * 5Step 2: Calculate the greatest common factor, GCF (also called greatest common divisor, GCD), by taking all the common prime factors of the numerator and denominator, by the lowest powers:gcd(2 * 31; 23 * 5) = 2 
Step 3: Divide both the numerator and denominator by their greatest common factor, GCF (also called the greatest common divisor, GCD):62/40 =
(2 * 31)/(23 * 5) =
((2 * 31) : 2) / ((23 * 5) : 2) =
31/(22 * 5) =
31/20Step 4: Improper fraction, rewrite:31 : 20 = 1 and remainder = 11 => 
31/20 = (1 * 20 + 11) / 20 = 1 + 11/20 = 1 11/20 as a mixed number (also called mixed fraction).1 + 11 : 20 = 1.55 as a decimal number.

6 0

3 years ago

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Which angles are supplementary to each other ? Select all that apply

swat32

Answer:

6 and 4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers