Our first wit of questions is relatesl to some haske exetcisss froan the required prerequisite backgronad in mathernaticx (Calculus I and Discrete Math). You should feel very confortable doing these Each question has erpual mark of [0.1 pts]. - Let f(x)=xexp(x3), what is the derivative of f(x) w.r.t x ? - Cousider an unfair coin that has probalsality 3/4 of conning up herals. If the coin is filpped three tinns, what is the probabality of secing trils ench time P(tails, fails, fails) = ? - I agree to let you flip the unfair coin (the same tufair coin as the previotes problem) obe time atad pay you $1 if it comes up hesds and $2 if it comes up taik. Leit X be the namber of dollars 1 pay yrat, which is a randon variable. What is the expected value of X:Z[X]= ? - Write the resalt of the following matrix-matrix maltiplicatioe. Your aasswer should be written in terms of t1,v, a, atd b. 272112[uvab] - Suppose (Bx+y)7A7=0, where A and B are both invertible nn mantrices and x and y are vectors in Rn, and 0 is a vector of all zeros. Use the properties of matrix anultiplication, transpose, and frverse to sbow that x=B1y. Shaw your work