Question

8. Let $X_1, X_2, \dots, X_n$ be positive, identically distributed random variables. For $1 \le i \le n$, let $Z_i = \frac{X_i}{X_1 + X_2 + \dots + X_n}$. Show that $Z_1, Z_2, \dots, Z_n$ are also identically distributed and, for $1 \le i \le n$, find $E(Z_i)$.

          8. Let $X_1, X_2, \dots, X_n$ be positive, identically distributed random variables. For $1 \le i \le n$, let

$Z_i = \frac{X_i}{X_1 + X_2 + \dots + X_n}$.

Show that $Z_1, Z_2, \dots, Z_n$ are also identically distributed and, for $1 \le i \le n$, find $E(Z_i)$.

8. Let X1, X2, …, Xn be positive, identically distributed random variables. For 1 ≤ i ≤ n, let

Zi = (Xi)/(X1 + X2 + … + Xn).

Show that Z1, Z2, …, Zn are also identically distributed and, for 1 ≤ i ≤ n, find E(Zi).

Added by Kenneth K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Nick Johnson

Step 1

.., Zₙ are identically distributed. To show that Z₁, Z₂, ..., Zₙ are identically distributed, we need to show that their probability distributions are the same. Since X₁, X₂, ..., Xₙ are identically distributed, it means that they have the same probability Show more…

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Let Xâ‚, Xâ‚‚, ..., Xâ‚™ be positive, identically distributed random variables. For 1 < i < n, let Záµ¢ = Xâ‚ + Xâ‚‚ + ... + Xâ‚™. Show that Zâ‚, Zâ‚‚, ..., Zâ‚™ are also identically distributed and, for 1 < i < n, find E(Záµ¢).