The second and fourth moment about mean for a distribution are 4 and 18 respectively. What is the value of Pearson's coefficient of skewness β z?
1.125
The question labels the coefficient as skewness but the only computable quantity from the given moments \(\mu_2\) and \(\mu_4\) is the Pearson kurtosis coefficient:
\[\beta_2 = \frac{\mu_4}{\mu_2^{2}} = \frac{18}{4^{2}} = \frac{18}{16} = \frac{9}{8} = 1.125\]
Hence the value is 1.125.
Similar Questions
The first four moments of a distribution about the value 2 are 1, 2.5, 5.5 and 16. What is the 4th moment about zero?
Given below are moments about an arbitrary origin 5.
If μ'1 = -4, μ'2 = 22, μ'3 = -117 and μ'4 = 560, then μ3 is equal to:The third order central moment of normal distribution is:
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Important Questions from Central Moments
The first four moments of a distribution about the value 2 are 1, 2.5, 5.5 and 16. What is the 4th moment about zero?
Given below are moments about an arbitrary origin 5.
If μ'1 = -4, μ'2 = 22, μ'3 = -117 and μ'4 = 560, then μ3 is equal to:The third order central moment of normal distribution is:
If μ'r and μr, respectively, denote rth order moments about origin and mean, then:
The standard deviation of a symmetrical distribution is 3. What must be the value of the fourth moment about the mean for the distribution to be mesokurtic?
