Suppose XK, K=1,2,3,4 are i.i.d. with X1 exponential with scale parameter 1. Consider: (I) X1+X2/X3+X4 has an F-distribution (II) X1+X2/X1+X2+X3 has a beta-distribution

Q130Section III (Statistics)130 of 180

Ratios of exponentials — $F$ and Beta

Suppose $X_K$ , $K=1,2,3,4$ are i.i.d. with $X_1$ exponential with scale parameter $1$ . Consider:

(I) $\dfrac{X_1+X_2}{X_3+X_4}$ has an $F$ -distribution
(II) $\dfrac{X_1+X_2}{X_1+X_2+X_3}$ has a $\beta$ -distribution

Pick an option to check your answer.

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