7 Do we have $\lim_{n\to \infty }\int X_n dP=\int\lim_{n\to \infty }X_ndP$ 5 A $\lambda$-system $\mathcal{L}$ that is a $\pi$-system is automatically a $\sigma$-field. 4 Show that the operator is invertible 3 How can we prove that $\frac{y'}{y}=(\ln y)'$? 3 Find the average value of $2x^2 + 5x + 2$ on the interval where $x \in [1,3]$.

### Reputation (2,006)

 +10 Joint pdf as a product of two independent functions with dependent domain +10 Show that the operator is invertible +5 probability theory, conditional probability +5 Example of product space isomorphic to sum of subspaces

### Questions (16)

 5 Example of product space isomorphic to sum of subspaces 4 Inner product equivalence 3 Limit of sum of independent simple functions 3 weak convergence of discrete uniform to lebesgue measure using characteristic functions 3 probability theory, conditional probability

### Tags (82)

 41 probability × 33 9 calculus × 6 24 measure-theory × 17 9 elementary-set-theory × 5 19 real-analysis × 31 8 statistics × 7 15 probability-theory × 16 7 random-variables × 8 10 integration × 7 7 limits × 5

### Account (1)

 Mathematics 2,006 rep 514