Probability, Random Variables and Density Functions
Not what you're looking for?
1. A coin is biased so that a head is three times as likely to occur as a tail. Find the expected number of tails when this coin is tossed twice.
2. An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, ¼, ¼, 1/6, and 1/6, respectively, that the attendant receives $7, $9, $11, $13, $15, or $17 between 4pm and 5pm on any sunny Friday. Find the attendant's expected earnings for this particular period.
3. If a dealer's profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function
f(x) = 2(1-x), 0 < x < 1,
0 elsewhere
Find the average profit per automobile.
4. What proportion of individuals can be expected to respond to a certain mail-order solicitation if the proportion X has the density function
f(x) = 2(x+2)/5, 0 < x < 1,
0 elsewhere
5. Suppose that the probabilities are 0.4, 0.3, 0.2, and 0.1, respectively, that 0, 1, 2 or 3 power failures will strike a certain subdivision in any given year. Find the mean and variance of the random variable X representing the number of power failures striking this subdivision.
6. The proportion of people who respond to a certain mail-order solicitation is a random variable X having the density function given in #4. Find the variance of X.
See attached file for full problem description.
Purchase this Solution
Solution Summary
Probability, Random Variables and Density Functions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.