Suppose that x and y are independent geometric(p) random variables and w = min{x, y }. calculate p(x = x | w = x) where x is some fixed positive integer. hint: first decide whether this probability should be equal to 1/2, larger than 1/2, or smaller than 1/2.

Find the required measurements of the following trapezoids. a = 8 cm b = 16 cm h = 10 cm

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?

Write the equation in logarithmic form e^x=403.429