20. Correct. The answer is false. To answer this question, it is necessary to calculate the skewness and kurtosis coefficients:

Skewness = . It consists of the third moment around the mean μ divided by the standard deviation powered to 3.

Kurtosis = . It consists of the fourth moment around the mean μ divided by the standard deviation powered to 4.

To compute these coefficients, it is firstly necessary to calculate the moments around the origin:

i) First moment around the origin: E[X] = μ = 2(0.4) + 4(0.3) + 6(0.2) + 8(0.1) = 4

ii) Second moment around the origin: E[X2] = 22(0.4) + 42(0.3) + 62(0.2) + 82(0.1) = 20

iii) Third moment around the origin: E[X3] = 23(0.4) + 43(0.3) + 63(0.2) + 83(0.1) = 116.8

iv) Fourth moment around the origin: E[X4] = 24(0.4) + 44(0.3) + 64(0.2) + 84(0.1) = 752.

Now, we have to calculate the central moments:

a) First central moment: E[X- μ] = 0

b) Second central moment: E[(X - μ)2] = E[X2] - μ2 = 20 - 42 = 4. This is the variance. The standard deviation is: σ = 2.

c) Third central moment: E[(X - μ)3] = E[X3] - 3*E[X]*E[X2] + 2*E[X]3

E[(X - μ)3] = 116.8 - 3(4)(20) + 2(4)3 = 4.8

d) Fourth central moment: E[(X - μ)4] = E[X4] - 4*E[X]*E[X3] + 6*E[X]2E[X2] - 3*E[X]4

E[(X - μ)4] = 752 - 4(4)(116.8) + 6(42)20 - 3(44) = 35.2

The skewness coefficient is: 4.8 / (23) = 0.60 implying the distribution is skewed to the right. It is not symmetric.

The kurtosis coefficient is: 35.2 / (24) = 2.2 implying the distribution has less kurtosis than the normal distribution which has kurtosis coefficient of 3. It means that the values of the distribution tend not to share the same frequency of occurrence. A coefficient of 2.2 means that the distribution is leptokurtic. A frequency function with coefficient of kurtosis greater than zero is said to be leptokurtic. It is more peaked about the mode than the normal distribution.