The area under the pdf between two values is the probability that the random variable lies between those two values.
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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
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.
yes, h=1/sigma(standard deviation)