TIFR ECE 2014 | Question: 13

Question

Let function $f: \mathbf{R} \rightarrow \mathbf{R}$ be convex, i.e., for $x, y \in \mathbf{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq$ $\alpha f(x)+(1-\alpha) f(y)$. Then which of the following is $\text{TRUE?}$

• A. $f(x) \leq f(y)$ whenever $x \leq y$.
• B. For a random variable $X, E(f(X)) \leq f(E(X))$.
• C. The second derivative of $f$ can be negative.
• D. If two functions $f$ and $g$ are both convex, then $\min \{f, g\}$ is also convex.
• E. For a random variable $X, E(f(X)) \geq f(E(X))$.