The cumulative distribution function of a random variable X is (see attached photo): a) What is P(X = 0)? b) What is P(X > 1)?
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!
The cumulative distribution
a) What is P(X = 0)?
b) What is P(X > 1)?
![The image presents a piecewise function \( F(x) \) defined as follows:
\[
F(x) =
\begin{cases}
0, & \text{when } x < 0 \\
\frac{1}{2}, & \text{when } 0 \leq x < 1 \\
1, & \text{when } x \geq 1
\end{cases}
\]
This means:
- \( F(x) = 0 \) for any value of \( x \) that is less than 0.
- \( F(x) = \frac{1}{2} \) for values of \( x \) that are greater than or equal to 0 but less than 1.
- \( F(x) = 1 \) for values of \( x \) that are greater than or equal to 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ccce870-cf0a-4230-85a3-2308c654cc66%2Fe6f1344a-0b03-4d19-8eda-9222590a9899%2Fju36mg_processed.jpeg&w=3840&q=75)
Given:-
we have to calculate
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