L"S~m][n '''dT~ l[ :][;] bo ordered bases for R2. Let v = [~] illld w = [~]. (a ) Find the coordinate vectors of v and w with respect to the basis T. (b) What is the trumition matrix Ps_r from the T- to the S-basis? (c) Find the coordinate veclors of v and w with respect to S.using 1'.1'_1 .(d) Find the coordinate lIectors of II and W with respectto 5 directly.(e) Find the transition matrix QT_ S from the 5 - to theT -basis.(I) Find the coordinate lIectors of II and w with respectto T. using Qr _ s. Compare the answers with thoseof (a

Probability 3.13.7 ● Randomness We call a phenomenon random if individual outcomes are uncertain. Chance behaviors unpredictable in the short run but has a regular and predictable pattern in the long run. ● Probability ○ The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. ○ If, under a given assumption, the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. ■ Classical method is use when all the experimental outcomes are equally likely. If n experimental outcomes are possible, a probability of 1/n is assigned to each experimental outcome. Example: Drawing a card from a standard deck of 52 cards. Each card has a 1/52 probability o ■ Relative frequency method is used when assigning probabilities is appropriate when data are available to estimate the proportion of the time the experimental outcome will occur if the experiment is repeated a large number of times. That is for any outcome, A, probability of A is ■ Subjective method