Consider the following real-valued functions F1 and F2 defined on R, given by F1(x)=1 if xge1 and F1(x)=0 otherwise, and F2(x)=int0^xexp(-t),dt if xge0 and F2(x)=0 otherwise. Define another function F:Rto[0,1] by F(x)=frac23F1(x)+frac13F2(x) for all xinR. Which of the following statements are true?

Q104Section C (Part C)104 of 120

Distribution functions — a mixture of a discrete and a continuous law

Consider the following real-valued functions $F_1$ and $F_2$ defined on $\mathbb{R}$ , given by $F_1(x)=1$ if $x\ge1$ and $F_1(x)=0$ otherwise, and $F_2(x)=\int_0^{x}\exp(-t)\,\mathrm{d}t$ if $x\ge0$ and $F_2(x)=0$ otherwise. Define another function $F:\mathbb{R}\to[0,1]$ by $F(x)=\frac23F_1(x)+\frac13F_2(x)$ for all $x\in\mathbb{R}$ . Which of the following statements are true?

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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