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When two dice are thrown let X be the larger of the two numbers on the two throws find the probability distribution mean and variance of X?
Wiki User
∙ 10y ago
The probability distribution is
P(X = 1) = 1/36
P(X = 2) = 3/36
P(X = 3) = 5/36
P(X = 4) = 7/36
P(X = 5) = 9/36
P(X = 6) = 11/36
P = 0 otherwise.
Mean(X) = 4.4722
Variance = 1.9715
Wiki User
∙ 10y ago
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When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Why the normal distribution can be used as an approximation to the binomial distribution?
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
The sample variance is always smaller than the true value of the population variance is always larger than the true value of the population variance could be smaller equal to or?
yes, it can be smaller, equal or larger to the true value of the population varience.
What is the probability that when two fair six sided dice are tossed the sun of the two numbers will be larger than 6?
21/36 = 7/12
What atmost means in probability?
all probabilities smaller than the given probability ("at most") all probabilities larger than the given probability ("at least")
Does a leptokurtic distribution have a larger variance than Mesokurtic distribution?
yes
Would one expect more variance with a larger sample size in a chi distribution?
The larger your sample size, the less variance there will be. For instance, your information is going to be much more substantial if you took 1000 samples over 10 samples.
When using the distribution of sample mean to estimate the population mean what is the benefit of using larger sample sizes?
The variance decreases with a larger sample so that the sample mean is likely to be closer to the population mean.
Can standard deviation be larger then its variance?
No. The standard deviation is the square root of the variance.
How does the number of repetitions effect the shape of the normal distribution?
When we discuss a sample drawn from a population, the larger the sample, or the large the number of repetitions of the event, the more certain we are of the mean value. So, when the normal distribution is considered the sampling distribution of the mean, then more repetitions lead to smaller values of the variance of the distribution.
Why the normal distribution can be used as an approximation to the binomial distribution?
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
The sample variance is always smaller than the true value of the population variance is always larger than the true value of the population variance could be smaller equal to or?
yes, it can be smaller, equal or larger to the true value of the population varience.
A probability can be no larger than what and no smaller than what?
A probability can be no larger than 1 and no smaller than 0.
Why do you square the deviations to get the variance and then take the reverse action of taking the square root of the variance to return the variance to sigma?
because of two things- a) both positive and negative deviations mean something about the general variability of the data to the analyst, if you added them they'd cancel out, but squaring them results in positive numbers that add up. b) a few larger deviations are much more significant than the many little ones, and squaring them gives them more weight. Sigma, the square root of the variance, is a good pointer to how far away from the mean you are likely to be if you choose a datum at random. the probability of being such a number of sigmas away is easily looked up.
What is Chi-square Probability Distribution?
The Chi-square probability distribution is a probability distribution that describes the distribution of the sum of squared standard normal random variables. It is often used in hypothesis testing and is characterized by its degrees of freedom. The shape of the distribution depends on the degrees of freedom parameter, with larger degrees of freedom resulting in a more symmetric and bell-shaped distribution.
What is the probability that when two fair six sided dice are tossed the sun of the two numbers will be larger than 6?
21/36 = 7/12
The probability of any outcome cannot be larger than which number?
larger than 1
