0
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
Construction of two random variables such that their correlation coefficient equals -1?
y = cos ( x ).
z = cos ( x + 180 degrees ).
Two 6 sided dice are rolled What is the probability the sum of the numbers is 12 or 4?
For a sum = 12, there's only one (6 + 6), 1/36
For a sum = 4, there's three: 2/36 (1 + 3) + 1/36 (2 + 2) = 3/36
Are events and its complement mutually exclusive?
Yes, they cannot happen at the same time. If you flip a coin heads and tails can not come up at the same time.
It is the probability distribution.
10/16 = .625
Analysis:
a and d will be odd if and only if both are odd. Therefor, ad will be odd 1/4 the time.
The same goes for bc. It will be odd 1/4 off the time.
ad-bc is even if and only if both ad and bc are either odd or even.
It's easiest to solve it from here with a table:
ad bc ad-bc prob
even even even 3/4*3/4 = 9/16
even odd odd 3/4*1/4 = 3/16
odd even odd 1/4*3/4 = 3/16
odd odd even 1/4*1/4 = 1/16
So, ad-bc will be even 9/16+1/16 = 10/16 of the time.
255/256 (complement formula)
It is (4/8)*(6/8) = 3/8
How many different ways can you arrange 15 cars in 12 parking spaces?
Any 12 from 15 in any order = 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 = 217,945,728,000 different ways!
This seems ridiculously high but...
The first space can be any one of fifteen, the second, any one of fourteen and so on until the twelfth can be any one of the remaining four.
8
hundredths
Factors that determine sample size?
1. population to deal with in the sample
2. Location. ocation where the sample will be done
3. design. how the sample will be taken
4. result. how the outcome will be determined
34.1% of the data values fall between (mean-1sd) and the mean.
What is the Standard deviation of a set of data in which all the data values are the same?
Zero
Details:
The "Standard Deviation" for ungrouped data can be calculated in the following steps:
- all the deviations (differences) from the arithmetic mean of the set of numbers are squared;
- the arithmetic mean of these squares is then calculated;
- the square root of the mean is the standard deviation
Accordingly,
- The arithmetic mean of set of data of equal values is the value.All the deviations will be zero and their squares will be zeros
- The mean of squares is zero
- The square root of zero is zero which equals the standard deion
What distribution does the F distribution approach as the sample size increases?
The F distribution is used to test whether two population variances are the same. The sampled populations must follow the normal distribution. Therefore, as the sample size increases, the F distribution approaches the normal distribution.
What is the probability of rolling a sum 10 with two dice?
3 times (out of 36) is the probablility
Possible Outcome 1 - Dice 1: 4, Dice 2: 6
Possible Outcome 2 - Dice 1: 5, Dice 2: 5
Possible Outcome 3 - Dice 1: 6, Dice 2: 4
Two coins are tossed What is the probability of both coins are heads?
The probability that both coins are heads is the probability of one coin landing heads multiplied by the probability of the second coin landing heads: (.5) * (.5) = .25 or (1/2) * (1/2) = 1/4
A standard normal distribution has a mean of and standard deviation of?
Mean 0, standard deviation 1.
