(Solved): Using this joint probability distribution function of random variables X and Y, find the probabil ...

Using this joint probability distribution function of random variables $X$ and $Y$, find the probability that $X=?10$ : $P(x,y)=?\begin{array}{lll}0.09\text{ if }x=?10,& y=?1& \\ 0.15& \text{ if }x=?5,& y=?1\\ 0.51& \text{ if }x=4,& y=?1\\ 0.05& \text{ if }x=?10,& y=100\\ 0.08\text{ if }x=?5,& y=100& \\ 0.12\text{ if }x=4,& y=100& \end{array}$ Enter TWO decimal places. Using this joint probability distribution function of random variables $B$ and $C$, find the probability that $B=1$ : $P(b,c)=?\begin{array}{lll}0.26\text{ if }b=?10,& c=?10& \\ 0.22& \text{ if }b=1,& c=?10\\ 0.26& \text{ if }b=?10,& c=?2\\ 0.06& \text{ if }b=1,& c=?2\\ 0.14& \text{ if }b=?10,& c=100\\ 0.06& \text{ if }b=1,& c=100\end{array}$ Enter TWO decimal places. Make use of this joint probability distribution function of random variables $S$ and $T$ to answer this question: $P(s,t)=?\begin{array}{ll}0.36\text{ if }s=1,& t=?4\\ 0.13\text{ if }s=2,& t=?4\\ 0.17\text{ if }s=20,& t=?4\\ 0.12\text{ if }s=1,& t=?2\\ 0.13\text{ if }s=2,& t=?2\\ 0.09\text{ if }s=20,& t=?2\end{array}$ Find $\mathbb{E}(S)$ Enter TWO decimal places. Using this joint probability distribution function of random variables $X$ and $Y$, find the probability that $X=4$ : $P(x,y)=?\begin{array}{ll}0.36\text{ if }x=?4,& y=?10\\ 0.23\text{ if }x=2,& y=?10\\ 0.03\text{ if }x=4,& y=?10\\ 0.21\text{ if }x=?4,& y=2\\ 0.12\text{ if }x=2,& y=2\\ 0.05\text{ if }x=4,& y=2\end{array}$ Enter TWO decimal places. Using this joint probability distribution function of random variables $S$ and $T$, find the probability that $S=3$ : $P(s,t)=?\begin{array}{lll}0.1& \text{ if }s=?1,& t=?10\\ 0.09& \text{ if }s=3,& t=?10\\ 0.08& \text{ if }s=50,& t=?10\\ 0.36& \text{ if }s=?1,& t=4\\ 0.23\text{ if }s=3,& t=4& \\ 0.14& \text{ if }s=50,& t=4\end{array}$ Enter TWO decimal places.