AMU 2026 — Mathematics PYQ

To determine the nature of the distribution, we calculate the coefficient of kurtosis, denoted as ${\beta }_2$, using the formula:

$${\beta }_2=\frac{{\mu }_4}{{\mu }_2^2}$$

Where:

• ${\mu }_2$ is the second central moment (variance) = $16$

• ${\mu }_4$ is the fourth central moment = $162$

1. Calculate ${\beta }_2$:

   $${\beta }_2=\frac{162}{(16{)}^2}$$

   $${\beta }_2=\frac{162}{256}$$

   $${\beta }_2=0.6328$$

2. Compare with the standard:

   In statistics, the kurtosis of a normal distribution is defined by ${\beta }_2=3$.

   • If ${\beta }_2=3$: Mesokurtic

   • If \beta_2 > 3: Leptokurtic

   • If \beta_2 < 3: Platykurtic

Since 0.6328 < 3, the distribution is Platykurtic (flatter than a normal distribution).