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What are characteristics of the X2?
It is not negative. it is positively skewed, and it approaches a normal distribution as the degrees of freedom increase. Its shape is NEVER based on the sample size.
What is Chi-square Probability Distribution?
Given Z~N(0,1), Z^2 follows χ_1^2 Chi-square Probability Distribution with one degree of freedom Given Z_i~N(0,1), ∑_(i=1)^ν▒Z_i^2 follows χ_ν^2 Chi-square Probability Distribution with ν degree of freedom Given E_ij=n×p_ij=(r_i×c_j)/n, U=∑_(∀i,j)▒(O_ij-E_ij )^2/E_ij follows χ_((r-1)(c-1))^2 Chi-square Probability Distribution with ν=(r-1)(c-1) degree of freedom Given E_i=n×p_i, U=∑_(i=1)^m▒(O_i-E_j )^2/E_i follows χ_(m-1)^2 Chi-square Probability Distribution with ν=m-1 degree of freedom
An ellipse in the plane has how many degrees of freedom?
five; they are: position, orientation, shape, and scale
What describes the shape of a distribution which is approximately normal?
A "bell" shape.
What is the shape of a z-score distribution?
The standard normal distribution or the Gaussian distribution with mean 0 and variance 1.
What are characteristics of the X2?
It is not negative. it is positively skewed, and it approaches a normal distribution as the degrees of freedom increase. Its shape is NEVER based on the sample size.
What happens to the shape of the chi-square distribution as the df value increases?
As the value of k, the degrees of freedom increases, the (chisq - k)/sqrt(2k) approaches the standard normal distribution.
How do you explain the characteristics of the F Distribution?
Characteristics of the F-distribution1. It is not symmetric. The F-distribution is skewed right. That is, it is positively skewed.2. The shape of the F-distribution depends upon the degrees of freedom in the numerator and denominator. This is similar to the distribution and Student's t-distribution, whose shape depends upon their degrees of freedom.3. The total area under the curve is 1.4. The values of F are always greater than or equal to zero. That is F distribution can not be negative.5. It is asymptotic. As the value of X increases, the F curve approaches the X axis but never touches it. This is similar to the behavior of normal probability distribution.
What is Chi-square Probability Distribution?
Given Z~N(0,1), Z^2 follows χ_1^2 Chi-square Probability Distribution with one degree of freedom Given Z_i~N(0,1), ∑_(i=1)^ν▒Z_i^2 follows χ_ν^2 Chi-square Probability Distribution with ν degree of freedom Given E_ij=n×p_ij=(r_i×c_j)/n, U=∑_(∀i,j)▒(O_ij-E_ij )^2/E_ij follows χ_((r-1)(c-1))^2 Chi-square Probability Distribution with ν=(r-1)(c-1) degree of freedom Given E_i=n×p_i, U=∑_(i=1)^m▒(O_i-E_j )^2/E_i follows χ_(m-1)^2 Chi-square Probability Distribution with ν=m-1 degree of freedom
Why t-distributions tend to be flatter and more spread out than normal distribution?
T-distributions tend to be flatter and more spread out than normal distributions due to their heavier tails. Unlike the normal distribution, which has thin tails, t-distributions account for uncertainty in sample variance estimation, making them more robust for smaller sample sizes. The additional variability inherent in t-distributions arises from the incorporation of the sample size through the degrees of freedom parameter. As the degrees of freedom decrease, the t-distribution becomes more spread out and flatter, reflecting increased uncertainty and variability in the estimates. This property makes t-distributions well-suited for inferential statistics, particularly when dealing with small sample sizes.
An ellipse in the plane has how many degrees of freedom?
five; they are: position, orientation, shape, and scale
What is the value of the degree of freedom?
The degree of freedom is a statistical measure that is the number of values in the final calculation of a statistic that are free to vary. It is important in determining the shape of the sampling distribution and is used in hypothesis testing and confidence interval estimation.
What shape describes a poisson distribution?
A skewed bell shape.
What describes the shape of a distribution which is approximately normal?
A "bell" shape.
How does the shape of the normal distribution differ from the shapes of the uniform and exponential distributions?
the normal distribution is a bell shape and expeonential is rectangular
What is the expected shape of the distribution of the sample mean?
The distribution of the sample mean is bell-shaped or is a normal distribution.
What is the shape of a z-score distribution?
The standard normal distribution or the Gaussian distribution with mean 0 and variance 1.
