Probability Distributions: Discrete and Continuous

The video tutorial introduces continuous probability distributions, also known as probability density functions (PDFs). It explains that PDFs specify the probability of a random variable within a range of values, as the probability of achieving an exact value is zero. The tutorial covers graphical representations of PDFs, properties of continuous distributions, and the use of integration to calculate probabilities. Example calculations are provided to find constants in PDFs, and the tutorial concludes with a summary of discrete and continuous distributions.

What is another name for a continuous probability distribution?

• Discrete probability function

• Cumulative distribution function

• Probability density function

• Probability mass function

Why is the probability of a continuous random variable taking an exact value zero?

• Because it is always positive

• Because it can only take integer values

• Because it can take any real number value

• Because it is defined over a finite range

How is the probability of a specified range of values for a continuous random variable determined?

• By using the mean of the distribution

• By calculating the area under the PDF curve

• By measuring the length of the range

• By counting the number of outcomes

What mathematical method is used to calculate the area under a probability density function?

• Integration

• Differentiation

• Summation

• Multiplication

In the given example, what is the value of the constant 'c' in the probability density function?

• 1/64

• 1/256

• 1/128

• 1/512

What is the probability that the random variable x is less than 7 in the given example?

• 0.45

• 0.77

• 0.57

• 0.67

What is the integral of a probability density function over its entire range equal to?

• 0.5

• 0

• 1

• 2