Search & Filtering
Show that for each a β M, the intersection V of all neighborhoods of a
equals {a} .
Show, by any suitable method, that every finite subset S of M is closed
Suppose that 2 batteries are randomly chosen without replacement from the following group of 9 batteries: 3 new, 4 used (working), 2 defective. Let X denote the number of new batteries chosen. Let Y denote the number of used batteries chosen. a. Find the joint probability distribution, π(π = π₯, π = π¦). b. Find πΈ[π].
For each day, independent of the others, the length of time for one individual to be served at
a cafeteria is a random variable having an exponential distribution with a mean of 4 minutes. What is the
probability that a person is served in less than 3 minutes on at least 4 of the next 6 days?
A parabolic satellite dish reflects signals to the dishβs focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function
ππ₯(π₯) = {π (1 β(1/16) π₯*2 , 0 < π₯ < 2
0, ππ‘βπππ€ππ π}
where X is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. Determine the following: a. Value of π that makes ππ₯(π₯) a valid probability density function.
b. π(0.1 < π < 0.4).
c. πΈ(π) and πππ(X)
The demand for a product, in dollars, is P=2000-0.2x-0.01x^2. Find the consumer surplus when the sales level is 250
Phenomena such as waiting times and equipment failure times are commonly modelled by exponentially decreasing probability density functions. Find the exact form of such a function
Researchers wish to test the effectiveness of a certain drug in lowering the cholesterol levels in individuals aged 50-60 years old. The mean cholesterol levels in previous researches for this age group is 250 mg/dL. The normal range is 200-239 mg/dL. 50 participants were invited to the study, The mean cholesterol levels for the participants after a month of taking the medication is 237 mg/dL with a standard deviation of 4 mg/dL. Assuming a normal distribution of times of labor, test at the 10% level of significance test whether the mean cholesterol level is less than 250 mg/dL.
There are fifteen students writing a Statistics exam. What is the probability of correctly
predicting the three students who obtain the highest marks in the exam, in the correct
order, assuming that no student obtains the same mark as any other student?
1. For each of the following relations, decide whether it is reflexive, whether it is symmetric or not, whether it is antisymmetric or not, and whether it is transitive or not on the set {1,2,3,4}? and why?
d) {(2,2), (3, 3)}
e) {(2,2), (1, 2), (3, 3)}
4. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,3), (2, 3), (2, 4), (3, 1),(3, 4), (3, 5), (4, 2), (4, 5), (5, 1), (5, 2), and (5, 4).
Find R 3 and R 4
7. Draw the directed graph that represents the relation {(a, a), (a, b), (b, c), (c, b), (c, d), (d, a), (d, b)}.
Β
8. list the ordered pairs in the relations represented by the directed graph.
