$A=\{0,1,2,3, \ldots\}$ is the set of non-negative integers. Let $F$ be the set of functions from $A$ to itself. For any two functions, $f_1, f_2 \in \mathrm{~F}$ we define

$$\left(f_1 \odot f_2\right)(n)=f_1(n)+f_2(n)$$

for every number $n$ in $A$. Which of the following is/are CORRECT about the mathematical structure $(\mathrm{F}, \odot)$ ?

Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is 0.01. Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is __________ ( (Rounded off to three decimal places)

Consider a probability distribution given by the density function $P(x)$.

$$P(x)=\left\{\begin{array}{cc} C x^2, & \text { for } 1 \leq x \leq 4 \\ 0, & \text { for } x<1 \text { or } x>4 \end{array}\right.$$

The probability that $x$ lies between 2 and 3, i.e., $P(2 \leq x \leq 3)$ is _________ (Rounded off to three decimal places)

Consider a demand paging memory management system with 32-bit logical address, 20 -bit physical address, and page size of 2048 bytes. Assuming that the memory is byte addressable, what is the maximum number of entries in the page table?