Question

question 12 (7 points)
construct a conditional distribution by x for the given contingency table. round values to the nearest thousandth.
x1 x2 x3
y1 40 40 25
y2 55 70 70

Explanation:

Step1: Calculate column totals

For \(x1\): \(40 + 55=95\)
For \(x2\): \(40+70 = 110\)
For \(x3\): \(25 + 70=95\)

Step2: Calculate conditional probabilities for \(y1\)

For \(x1\): \(\frac{40}{95}\approx0.421\)
For \(x2\): \(\frac{40}{110}\approx0.364\)
For \(x3\): \(\frac{25}{95}\approx0.263\)

Step3: Calculate conditional probabilities for \(y2\)

For \(x1\): \(\frac{55}{95}\approx0.579\)
For \(x2\): \(\frac{70}{110}\approx0.636\)
For \(x3\): \(\frac{70}{95}\approx0.737\)

Answer:

	\(x1\)	\(x2\)	\(x3\)
\(y2\)	\(0.579\)	\(0.636\)	\(0.737\)