Your lab is working to produce a particular chemical reaction. The conventional probability for producing this reaction successfully is p = ½. You have a new technique that you believe will produce this reaction successfully at least 2/3 of the time. You plan to test your method with a sequence of 36 trials. You decide to r
2.94 The joint probability function for the random variables X and Y is given in Table 2-9.... (see attached)
Problem 5. 1 out of 1000 births results in fraternal twins; 1 out of 1500 births results in identical twins. Identical twins must be the same sex, but the sexes of fraternal twins are independent. If two girls are twins, what is the probability that they are fraternal twins?
Suppose X had probability density function cx^2 for 0 < x < 1, 0 otherwise. Find (a) the constant c, and the (b) mean, and (c) variance fo X.
Problem 1. In the statements that follow, A and B are events in a sample space S with probability function P, X is a random variable defined on S, and a and b are constants. Mark T (true) if the statement is always true; F (false) if the statement is sometimes false. 1. 0 <= P(A) <= 1. 2. P(The union of A and B) + P(The in
A certain factory has three machines A,B and C that produces one type of light bulbs.Past experience has shown that the lifetime of a light bulb by machine A can be modeled as an exponential random variable with an average of 20 days, whereas the lifetime of a bulb produced by a machine B can modeled as a normal random variable
Suppose the number of electrons X counted by an optical communication system is a poisson random variable .(see the wholeproblem in the attachment)
Al, Bob and Carlos are playing a silly game. Al flips a coin. If he gets heads, the game ends and he wins. If not, Bob flips the coin. If he gets heads, the game ends and he wins. If not, Carlos flips the coin. If he gets heads, the game ends and he wins. If not, the coin is returned to Al and the entire process begins a
Al, Bob and Carlos are playing a silly game. Al flips a coin. If he gets heads, the game ends and he wins. If not, Bob flips the coin. If he gets heads, the game ends and he wins. If not, Carlos flips the coin. If he gets heads, the game ends and he wins. If not, the coin is returned to Al and the process begins again.
If n points are equally spaced on the circumference of a circle, what is the probability that three points chosen at random will form a right triangle? I know that for us to have a right triangle, the two points should form the diameter of the circle. What I have done is that I divided the problem into two sections. Section
It was suggested that the number of particles in a randomly selected interval might follow a Poisson distribution. Assuming a Poisson distribution to be an appropriate model for the data, use two methods to find an approximate 95% confidence interval for the mean of this distribution. See attachment for full question includin
Please see the attached file for full problem description. --- ? A sample of n independent observations are obtained of a random variable having a Poisson distribution with mean . Show that the maximum likelihood estimate of is he sample mean show that the corresponding estimator is an unbiased estimator of , and h
Constuct an unique pair of dice (6 sides) so that each of the sums 2 through 12 has an equal (nonzero i.e. cannot have two dice with all zero's) probability of occurring. The dice do not have to be identical.
If the probability that a woman is rich is 0.4, the probability that she is beautiful is 0.3 and the probability that she is either rich or beautiful is 0.5, what is the probability that she is both rich AND beautiful? Please show "all" steps to solution.
Question 1 A restaurant can serve up to 75 meals. Experience shows that 20% of clients who have booked do not turn up. 1. The manager accepts 90 bookings. What is the probability that more than 50 clients turn up? 2. How many bookings should the manager accept in order to have a probability of more than 0.9 that he will s
Problem Note: the problem is part of a thesis I'm working on. Define: > v > 0, where and v are parameters (constant). v < a < , where a is a parameter (constant). v1 - variable F(·) - probability distribution function with support [v, ]. f(·) = F'(·) - probability density function, strictly positiv
In the game of bridge, a player is dealt a hand of 13 playing cards from a standard 52 card deck. A hand is said to have a void in a suit if it contains no cards in that suit. Determine the number of distinct hands containing at least one void. What is the probability of being dealt a hand with at least one void? Your answer sho
4.19) The lifetimes of two car batteries (Brand A and B) are independent exponential random variables with means 12 hours and 10 hours, respectively. What is the probability that Brand B battery outlasts Brand A battery?
3.21) Suppose a machine has three independent components with Exp(.1) lifetimes. Compute the expected lifetime of the machine if it needs all three components to function properly. (This is a multivariate random variable problem)
2.54) Consider the k-out-of-n system (explanation: a system consists of n independent components. Each component functions with probability p. The system as a whole functions if at least k components are functioning (1 <= k <= n)). Suppose we visit this system at time t=3 and replace all failed components, at a cost of $75 eac
Suppose there are two vendors and each provides 50% of the items. The lifetime (in days) of an item from the first vendor is Exp(.1), and that from the second vendor is Exp(.08). Compute the probability that a randomly picked item will last more than 12 days.
2.16) Consider the k-out-of-n system (info on the system: A system consists of n independent components. Each component functions with probability p. The system as a whole functions if at least k components are functioning (1 <= k <= n)). The probability that a component is functioning at time t is given to be e^(-t). Comput
1.22) An oil executive has determined that the probability that this oil field contains oil is 0.6. Before starting the drilling she decides to order a seismological test to see if there is oil in the ground. Unfortunately, the test is not entirely accurate. It concludes that there is oil with probability 0.9 if there is indeed
In the questions I have below it says a bowl has eight ping pong balls numbered 1,2,2,3,4,5,5,5. You pick a ball at random. a. Find p(the number on the ball drawn is ≥ 3). b. Find p(the number on the ball drawn is even).
A jar contains 8 red marbles, 9 blue marbles, and 6 green marbles. Two marbles are chosen at random. What is the probability that one is green and the other is blue?
Let E and F be non-zero-probability events. If E and F are mutually-exclusive, can they also be independent? Explain the answer, and also prove it algebraically using the definitions of mutually-exclusive and independent events.
If E and F are events with P ( E U F ) = 5/8, P (E ∩ F = 1/3, and P (E) = ½, Find: (a) P(E) (E has a straight line over it) (b) P (F) (c) P (F) (F has a straight line over it) detail each answer: (a) ½ (b) 11/24 (c) 13/24
An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15% of individuals known to be cancer-free (false positive). One hundred individuals volunteer to take the test. Of the 100, 60 are known to have the cancer, and 40 are known
Peterson's vitamins, an advertiser in the magazine Healthy Living estimates that 1 Percent of the subscribers will buy vitamins from Petersons. They also estimate that 0.5 percent of nonsubscribers will buy the product and that there is one chance in 20 that a person is a subscriber. a) find the probability that a randomly sele
See attachment Newspaper article frequently cite the fact that in any one year a small percentage (say 10%) of all drivers are responsible for all automobile accidents. The conclusion is often reached that if only we could single out these accident-prone drivers and either retrain them or remove them from the reads we could d