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].
Given the probability density function f(x)
over the interval (2, 5], find the expected value, the mean,
3
the variance and the standard deviation.
Expected value:
Mean:
Variance:
Standard Deviation:
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
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