Question

Problem 4. 10 students choose between 3 schools A, B, C randomly (and independently). For each student, there is a $\frac{1}{2}$ chance of going to A, $\frac{1}{3}$ to B, and $\frac{1}{6}$ to C. Let $X_A$, $X_B$, $X_C$ be the number of students choosing A, B, C respectively. Find the pmf of the random vector ($X_A$, $X_B$, $X_C$). Determine whether $X_A$ and $X_B$ are independent.

Name: Problem 4. 10 students choose between 3 schools A, B, C randomly (and independently). For each student, there is a (1)/(2) chance of going to A, (1)/(3) to B, and (1)/(6) to C. Let XA, XB, XC be the number of students choosing A, B, C respectively. Find the pmf of the random vector (XA, XB, XC). Determine whether XA and XB are independent.
Uploaded: 2023-07-20T23:10:26-08:00
Duration: 4 min 33 s
Channel: Clarissa Barr
Description: Problem 4. 10 students choose between 3 schools A, B, C randomly (and independently). For each student, there is a (1)/(2) chance of going to A, (1)/(3) to B, and (1)/(6) to C. Let XA, XB, XC be the number of students choosing A, B, C respectively. Find the pmf of the random vector (XA, XB, XC). Determine whether XA and XB are independent.

          Problem 4. 10 students choose between 3 schools A, B, C randomly (and independently). For each student, there is a $\frac{1}{2}$ chance of going to A, $\frac{1}{3}$ to B, and $\frac{1}{6}$ to C. Let $X_A$, $X_B$, $X_C$ be the number of students choosing A, B, C respectively. Find the pmf of the random vector ($X_A$, $X_B$, $X_C$). Determine whether $X_A$ and $X_B$ are independent.

Problem 4. 10 students choose between 3 schools A, B, C randomly (and independently). For each student, there is a (1)/(2) chance of going to A, (1)/(3) to B, and (1)/(6) to C. Let XA, XB, XC be the number of students choosing A, B, C respectively. Find the pmf of the random vector (XA, XB, XC). Determine whether XA and XB are independent.

Added by Justin W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Clarissa Barr

07/20/2023

Step 1

Since each student chooses a school independently and randomly, we can model this situation using a multinomial distribution. The pmf of the multinomial distribution is given by: P(XA = k, XB = l, XC = m) = (10 choose k,l,m) * (1/2)^k * (1/3)^l * (1/6)^m where Show more…

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10 students choose between 3 schools A, B, C randomly (and independently). For each student,Problem 4. 10 students choose between 3 schools A,B,C randomly (and independently). For each student, there is a (1)/(2) chance of going to A,(1)/(3) to B, and (1)/(6) to C. Let x_(A),x_(B),x_(C) be the number of students choosing A,B,C respectively. Find the pmf of the random vector (x_(A),x_(B),x_(C)). Determine whether x_(A) and x_(B) are independent. there is a 1 2 chance of going to A, 1 3 to B, and 1 6 to C. Let XA, XB, XC be the number of students choosing A, B, C respectively. Find the pmf of the random vector (XA, XB, XC ). Determine whether XA and XB are independent. Problem 4. 10 students choose between 3 schools A,B,C randomly and independently). For each student there is a chance of going to A, to B, and to C. Let XA,X,Xc be the number of students choosing A,B,C respectively. Find the pmf of the random vector (XA,XB,Xc). Determine whether XA and X are independent.