65 ÷ 5 = 11 with 0 left over
Hope this helps! ;)
Answer:
![E(X) = 1*0.52+ 2*0.25 +3*0.23= 1.71](https://tex.z-dn.net/?f=%20E%28X%29%20%3D%201%2A0.52%2B%202%2A0.25%20%2B3%2A0.23%3D%201.71)
Now we can calculate the second moment with the following formula:
And replacing we got:
![E(X^2) = 1^2*0.52+ 2^2*0.25 +3^2*0.23= 3.59](https://tex.z-dn.net/?f=%20E%28X%5E2%29%20%3D%201%5E2%2A0.52%2B%202%5E2%2A0.25%20%2B3%5E2%2A0.23%3D%203.59)
And the variance is given by:
![Var(X) = E(X^2) -E(X)](https://tex.z-dn.net/?f=%20Var%28X%29%20%3D%20E%28X%5E2%29%20-E%28X%29)
And replacing we got:
![Var(X) = 3.59 -[1.71]^2 = 0.6659](https://tex.z-dn.net/?f=%20Var%28X%29%20%3D%203.59%20-%5B1.71%5D%5E2%20%3D%200.6659)
And the standard deviation is just the square root of the variance:
![Sd(X) = \sqrt{0.6659}= 0.816](https://tex.z-dn.net/?f=Sd%28X%29%20%3D%20%5Csqrt%7B0.6659%7D%3D%200.816)
Step-by-step explanation:
Previous concepts
For this case we define the random variable X =" how many children the couple will have" and we know the following distribution:
X 1 2 3
P(X) 0.52 0.250 0.230
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).
Solution to the problem
For this case we can find the expected value with the following formula:
![E(X) = \sum_{i=1}^n X_i P(X_i)](https://tex.z-dn.net/?f=%20E%28X%29%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20X_i%20P%28X_i%29)
And replacing we got:
![E(X) = 1*0.52+ 2*0.25 +3*0.23= 1.71](https://tex.z-dn.net/?f=%20E%28X%29%20%3D%201%2A0.52%2B%202%2A0.25%20%2B3%2A0.23%3D%201.71)
Now we can calculate the second moment with the following formula:
And replacing we got:
![E(X^2) = 1^2*0.52+ 2^2*0.25 +3^2*0.23= 3.59](https://tex.z-dn.net/?f=%20E%28X%5E2%29%20%3D%201%5E2%2A0.52%2B%202%5E2%2A0.25%20%2B3%5E2%2A0.23%3D%203.59)
And the variance is given by:
![Var(X) = E(X^2) -E(X)](https://tex.z-dn.net/?f=%20Var%28X%29%20%3D%20E%28X%5E2%29%20-E%28X%29)
And replacing we got:
![Var(X) = 3.59 -[1.71]^2 = 0.6659](https://tex.z-dn.net/?f=%20Var%28X%29%20%3D%203.59%20-%5B1.71%5D%5E2%20%3D%200.6659)
And the standard deviation is just the square root of the variance:
![Sd(X) = \sqrt{0.6659}= 0.816](https://tex.z-dn.net/?f=Sd%28X%29%20%3D%20%5Csqrt%7B0.6659%7D%3D%200.816)
Answer:
20, 35, 50
Step-by-step explanation:
For this case we have the following system of equations:
5x + 3y = 17
-8x - 3y = 9
We can rewrite the system like:
Ax = b
Where,
A = [5 3; -8 -3]
b = [17; 9]
x = [x; y]
The determinant of matrix A is given by:
lAl = ((5) * (- 3)) - ((3) * (- 8))
lAl = (-15) - (-24)
lAl = -15 + 24
lAl = 9
Answer:
The determinant for solving this linear system is:
lAl = 9
Answer:
$79.63
Step-by-step explanation:
You can figure this by estimating. 16% is a little less than 20%, which is 1/5. $497.69 is almost $500. So, 1/5 of that is almost $100, and a little less than that is about $80. The closest answer choice is $79.63.
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If you want to figure it exactly, you can do the multiplication ...
16% of $497.69 = 0.16 × $497.69 = $79.6304 ≈ $79.63