Problem

Find the proportion of observations of a standard…

01:38

Problem 6 Easy Difficulty

Find (a) the mean of the distribution, (b) the standard deviation of the distribution, and (c) the probability that the random variable is between the mean and 1 standard deviation above the mean.
The distance (in meters) that seeds are dispersed from a certain kind of plant is a random variable $x$ with probability density function defined by
$$
f(x)=0.1 e^{-0.1 x} \text { for } x \text { in }[0, \infty)
$$

Answer

$\begin{array}{llll}{\text { (a) } 10} & {\text { (b) } 10} & {\text { (c) } 0.2325}\end{array}$

Related Courses

Calculus 1 / AB

Finite Mathematics and Calculus with Applications

Chapter 18

Probability and Calculus

Section 3

Special Probability Density Functions

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Video Transcript

Okay, So for this question, we're giving a density function. F X is equal a 0.1 times e to the negative 0.1 times X for X from zero to infinity. We could notice. This follows exactly The format of the exponential distribution with Lambda equals 2.1. So if we want to find the expectation of X, which is the mean of our random variable, we know that that's going to be equal to one over Lambda. So one over 10.1, which is 10. Next. If we want to find the standard deviation, we know that's the square root of the variance. So that's going to be also one over Lambda for 10 again. Then if we want to find the probability that are variable is between its mean, which is 10 and one standard deviation above its mean, which would be 10 plus 10 for 20 we can look down here and see that that follows exactly the format for this formula, and that will give us point to 32 five. And these are going to be our final answers for this question.

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