Density Function of Random Variables
Not what you're looking for?
The destiny function for a random variable X is given in terms of constant c.....
Purchase this Solution
Solution Summary
The density function of random variables is examined.
Solution Preview
Since the integral of density function over the domain of X is equal to 1, we can find the value of c by
∫_(-∞)^∞▒〖δ(x)dx=1〗, or
∫_(-∞)^0▒〖ce^x dx+∫_0^∞▒〖ce^(-x) dx〗=1〗
ce^x |_(-∞)^0-ce^(-x) |_0^∞=1
c+c=1
So c=1/2
The distribution function is
If x<0,
∫_(-∞)^x▒〖1/2 e^t dt=1/2 e^t |_(-∞)^x 〗=1/2 e^x
If x≥0
∫_(-∞)^0▒〖1/2 e^t dt+∫_0^x▒〖ce^(-t) dt〗=1/2-1/2 e^(-t) |_0^x 〗=1-1/2 e^(-x)
In general format, the distribution function is
F(x)={█(〖1/2 e〗^x, x<0@1-1/2 e^(-x),x≥0)┤
P(X>1)=1-P(X≤1)=1-F(1)=1-1/2 e^(-1)=1-1/2e
P(-3<X≤4)=F(4)-F(-3)=1-1/2 e^(-4)-1/2 e^(-3)
P(X<-2)=F(-2)=1/2 e^(-2)=1/(2e^2 )
The graph of density function is
The graph of distribution function is
...
Purchase this Solution
Free BrainMass Quizzes
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.