4. Consider again the random variable with a cumulative distribution function of [5] F(x) = x² /25, for 0sx< 5. (a) What is the mean of this random variable? (b) What is the median of this random variable? (c) Find the 90th percentile of this random variable. (d) What is the probability of x =1? (e) Do you think x is a symmetric random variable? Why or why not?
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!
Consider again the random variable with a cumulative distribution
F(x) = x^2/25, for 0 ≤ x ≤ 5. (a) What is the mean of this random variable? (b) What is the
![4. Consider again the random variable with a cumulative distribution function of
[5]
F(x) = x²/25, for 0sx< 5. (a) What is the mean of this random variable? (b) What is the median
of this random variable? (c) Find the 90th percentile of this random variable. (d) What is the
probability of x =1? (e) Do you think x is a symmetric random variable? Why or why not?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b09b942-1721-4621-abc3-3e59df180c79%2Fbd601138-f09d-4865-8639-937fdecc777d%2F0tye7vk_processed.png&w=3840&q=75)
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