NIMCET 2026 — Mathematics PYQ

To classify the distribution based on kurtosis, we need to calculate the coefficient of kurtosis, denoted by ${\beta }_2$, which is defined as the ratio of the fourth central moment (${\mu }_4$) to the square of the variance (${\sigma }^2$).

Given data:

• Variance (${\sigma }^2$) = $3$

• Fourth central moment (${\mu }_4$) = $63$

The formula for ${\beta }_2$ is:

$${\beta }_2=\frac{{\mu }_4}{{\sigma }^4}=\frac{{\mu }_4}{({\sigma }^2{)}^2}$$

Substitute the values:

$${\beta }_2=\frac{63}{(3{)}^2}$$

$${\beta }_2=\frac{63}{9}$$

$${\beta }_2=7$$

Classification Criteria:

• If ${\beta }_2=3$, the distribution is Mesokurtic (Normal).

• If \beta_2 > 3, the distribution is Leptokurtic.

• If \beta_2 < 3, the distribution is Platykurtic.

Since ${\beta }_2=7$, which is greater than $3$, the distribution is Leptokurtic.

Correct Option: (a) Leptokurtic