A package contains two machinery components: a regular one and a defective one. An industrial robot chooses a component at random and the chosen undergoes an electrical and a mechanical extreme test. If the component is non-defective, it has 50% chance to pass the electrical test and 50% chance to pass the mechanical test; for the non-defective component the outcomes of the electrical and the mechanical test are entirely unrelated. In contrast, the defective component fails both tests with absolute certainty (100% probability of mechanical & electrical failure if defective). Consider now the following events. A= Electrical test results in failure.
B= Mechanical test results in failure.
C= Non-defective (regular) component has been selected.
Find the following probability figures:
(a) P(AIC)
(b) P(BIC)
(c) P(Aâ©BIC)
(d) P(A)
(e) P(B), and
(f) P(Aâ©B)
(g) Consider the statement "A and B are NOT independent, but they are conditionally independent given C."
Explain in detail what it means and decide if it is true or false.

In this problem, we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant. consider the data set 14, 6, 8, 15, 15. (a) use the defining formula, the computation formula, or a calculator to compute s. (round your answer to one decimal place.) s = 4.28 (b) multiply each data value by 3 to obtain the new data set 42, 18, 24, 45, 45. compute s. (round your answer to one decimal place.) s = 12.83 (c) compare the results of parts (a) and (b). in general, how does the standard deviation change if each data value is multiplied by a constant c? multiplying each data value by the same constant c results in the standard deviation remaining the same. multiplying each data value by the same constant c results in the standard deviation being |c| times as large. multiplying each data value by the same constant c results in the standard deviation increasing by c units. multiplying each data value by the same constant c results in the standard deviation being |c| times smaller. (d) you recorded the weekly distances you bicycled in miles and computed the standard deviation to be s = 3.8 miles. your friend wants to know the standard deviation in kilometers. do you need to redo all the calculations? yes no given 1 mile ≠1.6 kilometers, what is the standard deviation in kilometers? (enter your answer to two decimal places.)