Indicate whether each of the following statements is true (T) or false (F) - A continuous random variable takes on isolates values along the real line, usually integers. - Discrete random variables are random variables that can be measured to any degree of accuracy. This means that between every two possible values ? and ? there exists another possible value ?. - Distance travelled by a car on one litre of petrol is an example of a continuous random variable - We can use probability mass functions to describe mathematically discrete random variables. - A probability density function is used to describe mathematically a continuous random variable. - For any discrete probability distribution, ∑? ?(? ) = 1, for ?(? ) ≠ 0 - The time until the first occurrence (and between subsequent occurrences) follows an Exponential distribution.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Indicate whether each of the following statements is true (T) or false (F)
- A continuous random variable takes on isolates values along the real line, usually integers.
- Discrete random variables are random variables that can be measured to any degree of accuracy. This means that between every two possible values ? and ? there exists another possible value ?.
- Distance travelled by a car on one litre of petrol is an example of a continuous random variable
- We can use
- A probability density function is used to describe mathematically a continuous random variable.
- For any discrete probability distribution, ∑? ?(? ) = 1, for ?(? ) ≠ 0
- The time until the first occurrence (and between subsequent occurrences) follows an Exponential distribution.
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