If E(x) = 0.8, then the mean of the distribution is 0.8. You have not provided enough information to completely answer this question.
No. f is a letter of the Roman alphabet. It cannot be a probability density function.
A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.
what is density curve
Beyond the fact that they are both measures derived from probability density functions, I cannot think of any similarity.
Yes- the highest probability value is the mode. Let me clarify this answer: For a probability mass function for a discrete variables, the mode is the value with the highest probability as shown on the y axis. For a probability density function for continuous variables, the mode is the value with the highest probability density as shown on the y-axis.
Suppose the probability density function is f(x), defined over a domain D Then the mean is E(X) = x*f(x) integrated with respect to x over D. Calculate E(X2) = x2*f(x) integrated with respect to x over D. Then Variance(X) = E(X2) - [E(X)]2 and Standard Deviation = sqrt(Variance).
The modes of a probability density function might be defined as the (countable) set of points in the domain of the function for which the function achieves local maxima. Since the probability density function for the uniform distribution is constant by definition it has no local maxima, hence no modes. Hence, it cannot be bimodal.
No. f is a letter of the Roman alphabet. It cannot be a probability density function.
Normal distribution is the continuous probability distribution defined by the probability density function. While the binomial distribution is discrete.
A probability density function assigns a probability value for each point in the domain of the random variable. The probability distribution assigns the same probability to subsets of that domain.
probability density distribution
A Gaussian distribution is the "official" term for the Normal distribution. This is a probability density function, of the exponential family, defined by the two parameters, its mean and variance. A population is said to be normally distributed if the values that a variable of interest can take have a normal or Gaussian distribution within that population.
Probability Density Function
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.
what is density curve
A probability density function.
The probability mass function is used to characterize the distribution of discrete random variables, while the probability density function is used to characterize the distribution of absolutely continuous random variables. You might want to read more about this at www.statlect.com/prbdst1.htm (see the link below or on the right)