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A city temperature is modeled as a random variable with mean and standard deviation both equal to 10 degrees Celsius. A day is described as "normal" if the temperature during that day ranges within one standard deviation from the mean. What would be the temperature range for a normal day if temperature were expressed in degrees Fahrenheit?
A prize is randomly placed in one of ten boxes, numbered from 1 to 10. You search for the prize by asking yes-no questions. Find the expected number of questions until you a
Let X and Y be two random variables with given joint PMF, and let g and h be two functions of X and Y, respectively. Show that if X and Y are independent, then the same is t
Each paper receives a grade from the set {A, A-, B+. B, B-, C+}, with equal probability, independent of other papers. How many papers do you expect to hand in before you rec
Using Microsoft Excel, draw a graph illustrating the supply and demand in this market. Now suppose the government imposes a special tax on these computers. Describe what wou
A system consists of n identical components, each of which is operational with probability P. independent of other components. The system is operational if at least K out of
The king has only one sibling. What is the probability that the sibling is male? Assume that every birth results in a boy with probability 1/2, independent of other births.
How many 6-word sentences can be made using each of the 26 letters of the alphabet exactly once? A word is defined as a nonempty (possibly jibberish) sequence of letters.
We draw two balls randomly and simultaneously. Describe the sample space and calculate the probability that the selected balls are of different color, by using two approache
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