LetX1; X2; : : : ;be a sequence of inde-pendent identically distributed random variables. Assume that there are no ties. Wesay that a record occurs at timenifXn>max(X1; : : : ; Xn1). That is, Xnis arecord if it is larger than each ofX1; : : : ; Xn1. Show(i)Pfa record occurs at timeng= 1=n.(ii)E[number of records by timen] =∑ni=11=i.(iii)Var[number of records by timen] =∑ni=1(i1)=i2.Hint for (ii){(iii): At each timei, think about de ning some 1/0 variableYi, whichindicates whether there is a record at timei. Fori < j, what isPfYi= 1jYj= 1g?

$8

step-by-step explanation:

it is pretty much backwards.

you take the 4x2 multiply that, and that is = $8

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.