For each probability and percentile problem, draw the picture. the speed of cars passing through the intersection of blossom hill road and the almaden expressway varies from 11 to 35 mph and is uniformly distributed. none of the cars travel over 35 mph through the intersection. part (a)

in words, define the random variable x.

the speed, in mph, of an individual car passing through the intersectionthe time, in seconds, it takes a car to pass through the intersection the number of cars passing through the intersectionthe number of cars driving below 35 mph through the intersection

part (b)

give the distribution of x.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.