A random variable has a probability density function .f(x)=cx(6-x)2 0<=x<=6 and 0 otherwise . Calculate the arithmetic mean, variance and standard deviation of X r.v
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!
- A random variable has a probability density
function .f(x)=cx(6-x)2 0<=x<=6 and 0 otherwise
- . Calculate the arithmetic mean, variance and standard deviation of X r.v
2. In the tossing of three fair coins, let the random variable X be defined as X = number of tails. Then X can assume values 0, 1, 2, and 3.
- What is the probability distribution for the above scenario?
- Compute the
expected value X - Compute the standard deviation X
3.To find out the prevalence of smallpox vaccine use, a researcher inquired into the number of times a randomly selected 200 people aged 16 and over in an African village had been vaccinated. He obtained the following figures: never, 17 people; once, 30; twice, 58; three times, 51; four times, 38; five times, 7. Assuming these proportions continue to hold exhaustively for the population of that village, what is the expected number of times those people in the village had been vaccinated, and what is the standard deviation?
Step by step
Solved in 5 steps with 5 images
![2. Find a constant C such that the function
h(x) =
[Cx³ (1-x),
0,
for 0 ≤ x ≤ 1
otherwise
is a probability density function. Let X be a random variable with probability density function h(x). What
is E[X]? What is Var(X)?](https://content.bartleby.com/qna-images/question/1034590c-f69a-4c78-a8ec-21ce468ae083/ba121691-e32c-4566-a78f-5db82e841fa9/c6f7dtj_processed.jpeg)
by Bartleby Expert
