Ams 310 Survey Of Probability And Statistics Worksheet - Midterm Exam I - Stony Brook University Page 9
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11(7). A random variable can take seven values:
. The probability for
0, 1, 2, 3, 4, 5, 6
each value is
. Find the value of the parameter
. Find the
2
P (X = x) = C(x
3)
C
mathematical expectation (mean) and the variance of the random variable.
Since
Solution:
6
6
2
2
2
2
2
2
2
P (X = x) =
C(x
3)
= C(3
+ 2
+ 1
+ 0 + 1
+ 2
+ 3
) = 28C = 1,
=0
=0
hence
1
C =
28
The mathematical expection is
6
1
2
µ = E(X) =
x(x
3)
28
=0
The variance is
2
6
6
1
1
2
2
2
2
2
2
σ
= E(X
)
µ
=
x
(x
3)
x(x
3)
28
28
=0
=0
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