No, it resembles a normal distribution, but discrete.
sum --- Probability
2-----------1/36
3-----------2/36
4-----------3/36
5-----------4/26
6-----------5/36
7-----------6/36
8-----------5/36
9-----------4/36
10----------3/36
11----------2/36
12----------1/36
The statement is false. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.
Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.
Yes, the uniform probability distribution is symmetric about the mode. Draw the sketch of the uniform probability distribution. If we say that the distribution is uniform, then we obtain the same constant for the continuous variable. * * * * * The uniform probability distribution is one in which the probability is the same throughout its domain, as stated above. By definition, then, there can be no value (or sub-domain) for which the probability is greater than elsewhere. In other words, a uniform probability distribution has no mode. The mode does not exist. The distribution cannot, therefore, be symmetric about something that does not exist.
the variance of the uniform distribution function is 1/12(square of(b-a)) and the mean is 1/2(a+b).
Yes, except that if you know that the distribution is uniform there is little point in using the empirical rule.
No. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.
A discrete uniform distribution assigns the same probability to two or more possible events. For example, there is a discrete uniform distribution associated with flipping a coin: 'heads' is assigned a probability of 1/2 as is the event 'tails'. (Note that the probabilities are equal or 'uniform'.) There is also a discrete uniform distribution associated with tossing a die in that there is a 1/6 probability for seeing each possible side of the die.
The statement is false. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.
Don't know what "this" is, but all symmetric distributions are not normal. There are many distributions, discrete and continuous that are not normal. The uniform or binomial distributions are examples of discrete symmetric distibutions that are not normal. The uniform and the beta distribution with equal parameters are examples of a continuous distribution that is not normal. The uniform distribution can be discrete or continuous.
Assuming the uniform continuous distribution, the answer is 29/49. With the uniform discrete distribution, the answer is 29/50.
It could be a random variable with a discrete uniform distribution over the range 1 to 6.
Uniform probability can refer to a discrete probability distribution for which each outcome has the same probability. For a continuous distribution, it requires that the probability of the outcome is directly proportional to the range of values in the desired outcome (compared to the total range).
Uniform probability can refer to a discrete probability distribution for which each outcome has the same probability. For a continuous distribution, it requires that the probability of the outcome is directly proportional to the range of values in the desired outcome (compared to the total range).
I will assume that you are asking about probability distribution functions. There are two types: discrete and continuous. Some might argue that a third type exists, which is a mix of discrete and continuous distributions. When representing discrete random variables, the probability distribution is probability mass function or "pmf." For continuous distributions, the theoretical distribution is the probability density function or "pdf." Some textbooks will call pmf's as discrete probability distributions. Common pmf's are binomial, multinomial, uniform discrete and Poisson. Common pdf's are the uniform, normal, log-normal, and exponential. Two common pdf's used in sample size, hypothesis testing and confidence intervals are the "t distribution" and the chi-square. Finally, the F distribution is used in more advanced hypothesis testing and regression.
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Uniform distribution
Yes, the uniform probability distribution is symmetric about the mode. Draw the sketch of the uniform probability distribution. If we say that the distribution is uniform, then we obtain the same constant for the continuous variable. * * * * * The uniform probability distribution is one in which the probability is the same throughout its domain, as stated above. By definition, then, there can be no value (or sub-domain) for which the probability is greater than elsewhere. In other words, a uniform probability distribution has no mode. The mode does not exist. The distribution cannot, therefore, be symmetric about something that does not exist.