Probability

The relations depend on what measures.

The sample mean is an unbiased estimate for the population mean, with maximum likelihood.

The sample maximum is a lower bound for the population maximum.

You are correct; convenience sampling is not random sampling.

The probability of a club is 1/4 and the probability of a diamond is 1/4 so since they are mutually exclusive you just add them and the total probability is 1/2

Of course there are 4 suits, and clubs and diamonds are 2 of the 4 so we could have just said 1/2.

There are three odd numbers in a die: 1, 3, 5.

The probability of rolling an odd number in a fair die is: P(1 or 3 or 5) = 3/6 = 1/2

good

Yes, if you mean normal with a mean other than 0 and/or standard error other than 1.

If m is the mean and s the standard error, then transform the original data, y, using:

z = (y - m)/s

z will have the N(0,1) distribution!!!!!!!

The probability is 6/52 = 3/26.

From a 52 card deck, probability is 1/52.

There are 7!/4! = 210

2.27%

In a normal distribution half (50%) of the distribution falls below (to the left of) the mean.

The probability density function of a random variable can be either chosen from a group of widely used probability density functions (e.g.: normal, uniform, exponential), based on theoretical arguments, or estimated from the data (if you are observing data generated by a specific density function).

More material on density functions can be found by following the links below.

P(A given B')=[P(A)-P(AnB)]/[1-P(B)].

You should be given p(x) values such as 0.09 0.19 0.14 0.29 you just add these values to get 0.71 subtract 0.71 from 1 to get 0.29 is the answer

We would need to know the situation to respond to this question.

Empirical means by observation, so empirical probability, or experimental probability, is the probability that is observed in a set of trials. For example, if you flip a coin ten times and get seven heads, your empirical probability is 7 in 10. This is different than the theoretical probability, which for a fair coin is 5 in 10, but that result will only be approximated by the empirical results, and then only with a larger number of trials.

A large standard deviation indicates that the distribution is heavily weighted far from the mean. Take the following example:

{1,1,1,1,1,19,19,19,19,19} Mean is 10 and StDev = 9.49

Now look at this data set: {5, 6, 7, 8, 9, 11, 12, 13, 14, 15}

Mean is still 10, but StDev = 3.5

for residential building 1 sqm steel required =8kgs

1 in 32. Each correct answer has to rely on the previous answers all being correct. By random chance getting five heads in a row or picking black or red correctly, on a wheel with no green slots, five times in a row is 1 chance in 32 attempts.

3 ways

6 and 1.

3 and 4.

5 and 2.

27/35

The probability of HTTTT is (1/2)5 = 1/32

The correct flips can also be achieved with THTTT, TTHTT, TTTHT, & TTTTH.

Hence, total probability is 5/32.

They are effectively the same but the standard deviation is more popular because the units of measurement are the same as those for the variable.

The standard deviation is better since it takes account of all the information in the data set. However, the range is quick and easy to compute.

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