Assume a continuous uniform probability distribution over the range [47, 51.5]. what is the skewness of the probability distribution?

The skewness of the probability distribution is zero (0)

Step-by-step explanation:

The skewness is an statistical measure of the asymmetry of your data and your corresponding probability distribution around the mean value. When the probability density function has large values the distribution is positively skewed ( probability is concentrated in the right) and when it has low values is negatively skewed (probability is concentrated in the left). When the probability function is symmetrical around the mean, that means that the image at the left or right of the mean is identical,  the skew is zero. That's the case with the uniform probability distribution, because all values are equally probable, so the density function is identical by the left and right of the mean, no matter the initial value (in this case 47) or final value (in this case 51.5). When this occurs skewness is zero (see image).

x=6 and x=3

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1