For each probability density function, over the given interval, find E ( x ) , E ( x 2 ) , the mean, the variance, and the standard deviation. f ( x ) = 1 4 , [ 3 , 7 ]
For each probability density function, over the given interval, find E ( x ) , E ( x 2 ) , the mean, the variance, and the standard deviation. f ( x ) = 1 4 , [ 3 , 7 ]
Solution Summary: The author calculates the probability density function f(x)=14 over the interval [3,7].
Find the mean, E[X], and variance, E[X²] – E[X], of a Uniform[a, b] random variable.
: 'Example 7-37. A random variable X assumes the value 1, 12, ... with probabilities
U1, Uz ... respectively. Show that
1
u; e» (^;)* ; ^; > 0, Du; = 1
j=0
Pk
k!
=D0
Show full solution.According to rainfall data collected by a laboratory during storm events, the precipitation level in inches (X) varies jointly with runoff in cubic feet per second (Y). The joint probability mass function (PMF) of both variables are given by the following Table:
Y
1
2
3
10
0.05
0.15
0
20
0.1
0.25
0.25
30
0
0.1
0.1
a. What is the probability that the next storm will bring a precipitation of 2 or more inches and a runoff of more than 20 cfs?b. After a storm, a precipitation of 2 inches is measured. What is the probability that the runoff in this storm is 20 cfs or more?c. Are X and Y statistically dependent? Substantiate your answer.
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Continuous Probability Distributions - Basic Introduction; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=QxqxdQ_g2uw;License: Standard YouTube License, CC-BY
Probability Density Function (p.d.f.) Finding k (Part 1) | ExamSolutions; Author: ExamSolutions;https://www.youtube.com/watch?v=RsuS2ehsTDM;License: Standard YouTube License, CC-BY
Find the value of k so that the Function is a Probability Density Function; Author: The Math Sorcerer;https://www.youtube.com/watch?v=QqoCZWrVnbA;License: Standard Youtube License