Let X be a continuous random variable with a probability density function f and the moment generating function M(t). Suppose that f(x)=f(-x) for all xinR and the moment generating function M(t) exists for tin(-1,1). Then which of the following statements is/are correct?

Q35Section B (Section B)35 of 60

Consequences of an even density

Let $X$ be a continuous random variable with a probability density function $f$ and the moment generating function $M(t)$ . Suppose that $f(x)=f(-x)$ for all $x\in\mathbb{R}$ and the moment generating function $M(t)$ exists for $t\in(-1,1)$ . Then which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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