Fatigue Test Probability Analysis The following joint probability data apply to a fatigue test run on bronze strips. X represents cycles to failure (in 105) when alternate strips are bent at a high level of deflection. Y represents the same at a lower deflection event. **a. Find the marginal probabi
Fatigue Test Probability Analysis
The following joint probability data apply to a fatigue test run on bronze strips. X represents cycles to failure (in $10^5$) when alternate strips are bent at a high level of deflection. Y represents the same at a lower deflection event.
$$\begin{array}{c|cccc} X/Y & 20 & 30 & 40 & 50 \ \hline 4 & 0.01 & 0.03 & 0.05 & 0.02 \ 5 & 0.03 & 0.10 & 0.08 & 0.04 \ 6 & 0.02 & 0.08 & 0.12 & 0.11 \ 7 & 0.02 & 0.04 & 0.07 & 0.18 \ \end{array}$$
a. Find the marginal probability distribution for X and Y
b. Determine the conditional probability distribution of Y given $X = 5$
c. Are X and Y independent?
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Joint probability table $f(x,y)$: X/Y 20 30 40 50 ------------------------- 4 0.01 0.03 0.05 0.02 5 0.03 0.10 0.08 0.04 6 0.02 0.08 0.12 0.11 7 0.02 0.04 0.07 0.18 Marginal of X: $P(X=x)=\sumy f(x,y)$ $$P(X=4)=0.01+0.03+0.05+0.02=0.11$$ $$P(X=5)=0.03+0.10+0.08+0.04=0.25$$ $$P(X=6)=0.02+0.08+0.12+...