Kindly answer question 2 Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classificationof Y = {0, 1} with Y= 1 indicating a positive result:X~ Ber(p)Y | X Ber(px)2. Find the Cov(Y, X) in terms of p, p₁, and po.

Given information: X∈0,1 with X=1 indicating disease. Y∈0,1 with Y=1 indicating a positive result.…

Answered: Given X = {0, 1} with X = 1 indicating…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Kindly answer question 2

Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classification
of Y = {0, 1} with Y= 1 indicating a positive result:
X~ Ber(p)
Y | X Ber(px)
2. Find the Cov(Y, X) in terms of p, p₁, and po.

Expert Solution

Step 1

Given information:

$X \in \{0, 1\} w i t h X = 1 i n d i c a t i n g d i s e a s e$ .

$Y \in \{0, 1\} w i t h Y = 1 i n d i c a t i n g a p o s i t i v e r e s u l t$ .

$X ~ B e r (p)$

$P (X = x) = p^{x} {(1 - p)}^{1 - x}, x = 0, 1$

X	0	1
P(X)	$p^{0} {(1 - p)}^{1 - 0} = 1 - p$	$p^{1} {(1 - p)}^{1 - 1} = p$

$Y | X ~ B e r (p_{x})$

$P (Y | x) = {(p_{x})}^{y} {(1 - p_{x})}^{1 - y}, x = 0, 1 a n d y = 0, 1$

If Y=0, X=0,

$P (Y = 0 | X = 0) = {(p_{0})}^{0} {(1 - p_{0})}^{1 - 0} = 1 - p_{0}$

If Y=0, X=1,

$P (Y = 0 | X = 1) = {(p_{1})}^{0} {(1 - p_{1})}^{1 - 0} = 1 - p_{1}$

If Y=1, X=0,

$P (Y = 1 | X = 0) = {(p_{0})}^{1} {(1 - p_{0})}^{1 - 1} = p_{0}$

If Y=1, X=1,

$P (Y = 1 | X = 1) = {(p_{1})}^{1} {(1 - p_{1})}^{1 - 1} = p_{1}$

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Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classification of Y = {0, 1} with Y= 1 indicating a positive result: X~ Ber(p) Y | X Ber(px)