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Probability
The probability of a certain event is a number expressing the likelihood that a specific event will occur, expressed as the ratio of the number of actual occurrences to the number of possible occurrences. In mathematics, it is a measure of how often an event will happen and is the basis of statistics.
14,643 Questions
It is 5C1*(1/10)1*(9/10)4 = 0.3281
This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.
Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,
For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:
However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.
A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint and
Sets that are not the same.
What is the number of marbles left in a 48-marble bag after some marbles have been givin away?
The number of marbles left in a 48 marble bag after some number N marbles have been given away is 48-N.
What are two ways mesopotamia and shang-china were similar and two ways they were different?
they are the same in politics and social structure, but they are different in politics
4:6 which equals 2:3 and 1:1.5
or in decimal 0.666667
What is the sample space of a coin tossed n times?
The sample space consists of 2n ordered n-tuples of the form (X1, X2, ..., Xn) where each Xi = H or T.
What is obtained by squaring the standard deviation?
Variance. Although usually it is the SD that is calculated from the variance.
How many different 13-card bridge hands can be selected from an ordinary deck?
This is a combinations question. There are (52 C 13) possible hands. This is 52!/((13!)((52-13)!)) = 635013559600
24
The first letter can be any of the 4. The second can be any of the remaining 3. The third, either remaining, and the last, the only remaining one. This means there are 4*3*2*1=24 different arrangements.
If the standard deviation decreases does the mean decrease?
Not necessarily. The standard deviation measures (in simplified terms) how different the numbers are from each other, while the mean is their average. If the standard deviation decreases, it means the numbers are closer to each other, it doesn't change how big the numbers are.
Bradford Services Inc. (BSI) is considering a project that has a cost of $10 million and an expected life of 3 years. There is a 30 percent probability of good conditions, in which case the project will provide a cash flow of $9 million at the end of each year for 3 years. There is a 40 percent probability of medium conditions, in which case the annual cash flows will be $4 million, and there is a 30 percent probability of bad conditions and a cash flow of -$1 million per year. BSI uses a 12 percent cost of capital to evaluate projects like this.
a. Find the project\'s expected cash flows and NPV.
b. Now suppose the BSI can abandon the project at the end of the first year by selling it for $6 million. BSI will still receive the Year 1 cash flows, but will receive no cash flows in subsequent years. Assume the salvage value is risky and should be discounted at the WACC.
c. Now assume that the project cannot be shut down. However, expertise gained by taking it on will lead to an opportunity at the end of Year 3 to undertake a venture that would have the same cost as the original project, and the new project\'s cash flows would follow whichever branch resulted for the original project. In other words, there would be a second $10 million cost at the end of Year 3, and then cash flows of either $9 million, $4 million, or -$1million for the following 3 years. Use decision tree analysis to estimate the value of the project, including the opportunity to implement the new project in Year 3. Assume the $10 million cost at Year 3 is known with certainty and should be discounted at the risk-free rate of 6 percent. Hint: do one decision tree for the operating cash flows and one for the cost of the project, then sum their NPVs.
d. Now suppose the original (no abandonment and no additional growth) project could be delayed a year. All the cash flows would remain unchanged, but information obtained during that year would tell the company exactly which set of demand conditions existed. Use decision tree analysis to estimate the value of the project if it is delayed by 1 year. Hint: Discount the $10 million cost at the risk-free rate since it is known with certainty. Show two time lines, one for operating cash flows and one for the cost, then sum their NPVs.
e. Go back to part c. Instead of using decision tree analysis, use the Black-Scholes model to estimate the value of the growth option. The risk-free rate is 6 percent, and the variance of the project\'s rate of return is 22 percent.
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What is the probability of an electron state being filled if it is at the fermi level?
1/2 independent from temperature
What conditions are required to form a valid large-sample confidence interval for you?
1) What conditions are required to form a valid large-sample confidence interval for µ?
What does the complement rule state?
Event A denotes the complement of event A, meaning that Ā consists of all outcomes in which event A does not occur. Event A and Ā must be disjoint, because it is impossible for an event and its complement to occur at the same time.
When would the standard deviation of a data set be zero?
Either when there is a single data item, or when all data items have exactly the same value.
Why do deviation in a data set sum to zero?
They don't necessarily. Deviations from the median in an asymmetric data set will not sum to 0.
The mean is the sum of observations divided by the number of observations and some simple algebra will show that the sum of deviations from this equals 0. Unfortunately, the browser used by this site is useless for showing such work.
What does sample to draw an inference about the population mean?
you just put the phone number in it the push dile
What is a probability of an event?
Lets first start by defining some terms:
Probability (P) in statistics is defined as the chance of an event occurring.
Probability experiment is a chance process that leads to results called outcomes.
An outcome is the result of a single trial of a probability experiment.
A sample set is the set of all possible outcomes of a probability experiment.
An event consists of a set of outcomes of a probability experiment. An event can be one outcome or more than one outcome. The event can be anything from flipping a coin, to rolling a die, to picking a card.
The probability of any event (E) is:
(# of outcomes in E) / (total # of outcomes in sample space)
For example: Find the probability a die is rolled and you get a 4?
We know that there are 6 possibilities when rolling a die. We can either rolled a 1, or a 2, or a 3, or a 4, or a 5, or a 6.
Using the equation above:
P(rolling a 4)= 1/6
The event in this case is rolling a 4.
How do you find the standard deviation for the given probability distribution?
If the probability distribution function for the random variable X is f(x), then
first calculate E(X) = integral of x*f(x)dx over the whole real line.
Noxt calculate E(X2) = integral of x2*f(x)dx over the whole real line.
Then Variance(X) = E(X2) - [E(X)]2
and finally, SD(X) = sqrt[Variance(X)].
