Find the mean and variance of the random variable X with probability function or density f(x)
The value of k is got by noting that the Total Probability = 1.
Thus, we get:
between limits -1 to 1.
Applying limits, we get:
So,
k = 0.75
So,
The probability density function is:
,
for -1x1
Mean = E(X) is got as follows:
between the limits - 1 to 1
Applying limits, we get:
E(X) = 0
E(X2) is got as follows:
Applying limits, we get:
Variance = E(X2) - (E(X))2
= 0.2 - 02
= 0.2
So,
Answers are:
Mean = 0
Variance = 0.2
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