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Q49Section C (Section C)49 of 60

Limit in probability of the sample mean of a mixture

Let X1,X2,…,XnX_1,X_2,…,X_n be a random sample from the distribution with the probability density function

f(x)=14e−∣x−4∣+14e−∣x−6∣,x∈R.f(x)=\frac14e^{-|x-4|}+\frac14e^{-|x-6|},\quad x\in\mathbb R.

Then 1n∑i=1nXi\frac1n\sum_{i=1}^nX_i converges in probability to ____________

Numerical answer: type the number (no options).

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